Magnetic moment due to the motion of the electron in n t h orbit of hydrogen atom is proportional to
The following diagram indicates the energy levels of a certain atom when the electron moves from 4E level to E. A photon of wavelength λ 1 is emitted. The wavelength of photon produced during its transition from 7 3 E level to E is λ 2 . The ratio λ 1 λ 2 will be
In hydrogen and hydrogen-like atoms, the ratio of E 4 n − E 2 n and E 2 n − E n varies with atomic number z and principal quantum number n as
Which energy state of the triply ionized beryllium (Be +++ ) has the same electron orbital radius as that of the ground state of hydrogen? Given Z for beryllium = 4.
Hydrogen atoms are excited from ground state to the state of principal quantum number 4. Then, the number of spectral lines observed will be
If wavelength of photon emitted due to transition of an electron from the third orbit to the first orbit in a hydrogen atom is λ then the wavelength of photon emitted due to transition of electron from the fourth orbit to the second orbit will be
In figure, E 1 to E 6 represent some of the energy levels of an electron in the hydrogen atom. Which one of the following transitions produces a photon of wavelength in the ultraviolet region of the electromagnetic spectrum?
According to Bohr’s theory of hydrogen atom, the product of the binding energy of the electron in the nth orbit and its radius in the n th orbit
X-rays emitted from a copper target and a molybdenum target are found to contain a line of wavelength 22.85 nm attributed to the K α line of an impurity element. The K α lines of copper (Z = 29) and molybdenum (Z = 42) have wavelengths 15.42 nm and 7 .12 nm, respectively. The atomic number of the impurity element is
An electron in H atom makes a transition from n = 3 to n = 1. The recoil momentum of H atom will be
In interpreting Rutherford’s experiments on the scattering of alpha particles by thin foils, one must examine what the known factors were, and what the experiment concluded. Which of the following is true in this context?
When the hydrogen atom emits a photon in going from n = 5 to n = 1 state, its recoil speed is nearly
If the K α radiation of Mo (Z = 42) has a wavelength of 0.71 Å the wavelength of the corresponding radiation of Cu (Z = 29)
Which of the following statements are true regarding Bohr’s model of hydrogen atom? I. Orbiting speed of electron decreases as it shifts to discrete orbits away from the nucleus II. Radii of allowed orbits of electron are dependent on the principal quantum number III. Frequency with which electron orbits around the nucleus in discrete orbits is dependent on principal quantum number. IV. Binding force with which the electrons are bound to the nucleus increases as it shifts to outer orbits.
Suppose an electron is attracted towards the origin by a force k r , where, k is a constant and r is the distance of the electron from the origin. By applying Bohr’s model to this system, the radius of the n t h orbital of the electron is found to be r n and the kinetic energy of the electron to be T n . Then, which of the following is true?
Among the following identify the source which produces X-rays.
Emission spectrum of CO 2 gas
Missing lines in a continuous spectrum reveal
A neon sign does not produce
The first member of the Balmer series of hydrogen atom has a wavelength of 6561 A 0 . The wavelength of the second member of the Balmer series (in nm) is —-
A particle of mass 200 M e V / c 2 collides with a hydrogen atom at rest. Soon after the collision the particle comes to rest, and the atom recoils and goes to its first excited state. The initial kinetic energy of the particle i n e V i s N 4 . The value of N is: (Given the mass of the hydrogen atom to be 1 G e V / c 2 )
An energy of 24.6 eV is required to remove one of the electrons from a neutral helium atom. The energy (in eV) required to remove both the electrons from a neutral helium atom is
The transition from the state n=4 to n=3 in a hydrogen like atom results in ultraviolet radiation. Infrared radiation will be obtained in the transition
If the series limit of Lymen series for Hydrogen atom is equal to the series limit of Balmer series for a hydrogen like atom, then atomic number of this hydrogen-like atom will be
Consider a hydrogen like atom whose energy in n t h excited state is given by E n = − 13.6 Z 2 n 2 . When this excited atom, makes a transition from excited state to ground state, most energetic photons have energy E max = 52.224 eV and least energetic photons have energy E m i n = 1 .224 eV . The atomic number of atom is
The electron in a hydrogen atom makes a transition from an excited state to the ground state. Which of the following statements is true
The force acting on the electron in a hydrogen atom depends on the principal quantum number as
In Bohr’s model of hydrogen atom, let PE represent potential energy and TE the total energy. In going to a higher orbit,
When an electron jumps from n 1 t h orbit to n 2 t h orbit, the energy radiated is given by
If the electron in an hydrogen atom jumps from an orbit with level n i = 3 to an orbit with level n f = 2 the emitted radiation has a wavelength given by
The energy of an electron in an excited hydrogen atom is -3.4 eV. Then, according to Bohr’s Theory the angular momentum of this electron, in J s, is
As the quantum number increases, the difference of energy between consecutive energy levels:
The ionization potential of H atoms is 13.6 V. The energy difference between n = 2 and n = 3 levels is nearest to
In a hydrogen atom, the electron is in n t h excited state. It comes down to the first excited state by emitting 10 different wavelengths. The value of n is
In a hydrogen atom, the transition takes place from n = 3 to n = 2. If Rydberg’s constant is 1.09 × 10 7 m − 1 , the wavelength of the line emitted is
Let the potential energy of a hydrogen atom in the ground state be zero. Then, its energy in the first excited state will be
The orbital velocity of an electron in the ground state is v. If the electron is excited to energy state -0.54 eV, its orbital velocity will be
The ratio of maximum to minimum possible radiation energy in Bohr’s hypothetical hydrogen atom is equal to
In which of the following systems will the radius of the first orbit (n=1) be minimum?
If R is the Rydberg constant for hydrogen, then the wave number of the first line in the Lyman series is
If the series limit wavelength of the Lyman series for hydrogen atom is 912 Å , then the series limit wavelength for the Balmer series for the hydrogen atom is
The wavelength of the first line of Lyman series in hydrogen atom is 1216. The wavelength of the first line of Lyman series for 10 times ionized sodium atom will be added
A sample of hydrogen is bombarded by electrons. Through what potential difference should the electrons be accelerated so that third line of Lyman series be emitted?
Magnetic field at the center (at nucleus) of the hydrogen like atoms (atomic number = z) due to the motion of electron in n t h orbit is proportional to
An atom emits a spectral line of wavelength λ when an electron makes a transition between levels of energy E 1 and E 2 . Which expression correctly relates λ , E 1 and E 2 ?
A hydrogen-like atom emits radiations of frequency 2.7 × 10 15 Hz when it makes a transition from n = 2 to n = 1. The frequency emitted in a transition from n = 3 to n = 1 will be
If λ 1 and λ 2 are the wavelengths of the first members of the Lyman and Paschen series, respectively, then λ 1 : λ 2 is
An electron revolving in an orbit of radius 0.5 Å in a hydrogen atom executes 10 16 revolutions per second. The magnetic moment of electron due to its orbital motion will be
A beam of electron accelerated by a large potential difference V is made to strike a metal target to produce X-rays. For which of the following values of V, will the resulting X-rays have the lowest minimum wavelength?
The energy ratio of two K α photons obtained in X-ray from two metal targets of atomic numbers Z 1 and Z 2 is
The total energy of an electron in the ground state of hydrogen atom is -13.6 eV. The potential energy of an electron in the ground state of Li 2+ ion will be
If scattering particles are 56 for 90 o angle then find the number of particles at 60 o angle.
Consider a hydrogen like atom whose energy in n th excited state is given by E n = − 13.6 Z 2 n 2 when this excited atom makes a transition from excited state to ground state, most energetic photons have energy E max = 52.2224 eV and least energetic photons have energy E min = 1.224 eV . What is the atomic number of atom?
Find the ratio of ionization energy of hydrogen-like lithium atom and Bohr’s hydrogen atom.
Find the ratio between total acceleration of the electron in singly ionized helium atom and hydrogen atom (both in ground state).
K α wavelength emitted by an atom of atomic number Z = 11 is λ . The atomic number for an atom that emits K α radiation with wavelength 4 λ is
Among the following identify the source which produces X-rays.
The wavelength of K α X-rays produced by an X-ray tube is 0.76 A o . What is the atomic number of the anode material of the tube?
Line spectrum was first of all theoretically explained by
Line spectrum contains information about
The solar spectrum during a complete solar eclipse is
The time period of revolution of electron in its ground state orbit in a hydrogen atom is 1.6 × 10 − 16 s. The frequency of revolution of the electron in its first excited state i n s − 1 is
The graph which depicts the results of Rutherford gold foil experiment with α – particles is: θ : Scattering angle Y: Number of scattered α -particles detected (Plots are schematic and not to scale)
The energy required to ionize a hydrogen like ion in its ground state is 9 Rydberg. What is the wavelength of the radiation emitted when the electron In this ion jumps from the second excited state to the ground state?
In a hydrogen atom the electron makes a transition from (n + 1)th level to the nth level. If n >> 1, the frequency of radiation emitted is proportional to:
In the line spectra of hydrogen atom, difference between the largest and the shortest wavelenths of the Lyman series is 304 A 0 . The corresponding difference for the Paschan series in A 0 is : .
A double charged lithium atom is equivalent to hydrogen whose atomic number is 3. The wavelength of required radiation for emitting electron from first to third Bohr orbit in L i + + will be (Ionization energy of hydrogen atom is 13.6 eV)
Imagine an atom made up of a proton and a hypothetical particle of double the mass of the electron but having the same charge as the electron. Apply the Bohr’s atomic model and consider all possible transitions of this hypothetical particle to the first excited level. The longest wavelength photon that will be emitted has wavelength λ (given in terms of the Rydberg constant R for the hydrogen atom) equal to
The electric potential between a proton and an electron is given by V = V 0 ln r r 0 , where r 0 is a constant. Assuming Bohr’s model to be applicable, write the variation of r n , n being the principal quantum number
A hydrogen like atom of atomic number Z is in an excited state of quantum number 2n. It can emit a maximum energy photon of 204 eV. If it makes a transition to quantum state n, a photon of energy 40.8 eV is emitted. The value of n will be
The wavelength K α X-rays produced by an X-ray tube is 0.76 Å . The atomic number of anticathode material is
Energy levels A, B, C of a certain atom corresponding to increasing values of energy i.e. E A < E B < E C . If λ 1 , λ 2 , λ 3 the wavelengths of radiations corresponding to the transitions C to B, B to A and C to A, respectively, which of the following statements is correct
In hydrogen atom, if the difference in the energy of the electron in n=2 and n=3 orbits is E, the ionization energy of hydrogen atom is
The first line in the Lyman series has wavelength λ . The wavelength of the first line in Balmer series is
The energy required to excite an electron from the ground state of hydrogen atom to the first excited state, is
The minimum energy to ionize an atom is the energy required to
Which of the following is true when Bohr gave his model for hydrogen atom?
Angular momentum (L) and radius (r) of a hydrogen atom are related as
The angular momentum of an electron in an orbit is quantized because it is a necessary condition for the compatibility with
The maximum angular speed of the electron of a hydrogen atom in a stationary orbit is
The energy change is greatest for a hydrogen atom when its state changes from
The electron in a hydrogen atom jumps from the ground state to the higher energy state where its velocity is reduced to one-third of its initial value. If the radius of the orbit in the ground state is r, the radius of new orbit will be
If 13.6 eV energy is required to ionize the hydrogen atom, then the energy required to remove an electron from n = 2 is
If the radius of an orbit is r and the velocity of electron in it is v, then the frequency of electron in the orbit will be
The potential energy of an electron in the fifth orbit of hydrogen atom is
The ratio of the speed of the electron in the first Bohr orbit of hydrogen and the speed of light is equal to (where e, h, and c have their usual meanings in cgs system)
The radius of the Bohr orbit in the ground state of hydrogen atom is 0.5 A. The radius of the orbit of the electron in the third excited state of H e + will be
Which of the following parameters are the same for all hydrogen-like atoms and ions in their ground states?
The ionization energy of the ionized sodium atom N a 10 + is
The ratio between total acceleration of the electron in singly ionized helium atom and hydrogen atom (both in ground state) is
Let v 1 be the frequency of series limit of Lyman series, v 2 the frequency of the first line of Lyman series, and v 3 the frequency of series limit of Balmer series. Then which of the following is correct?
A stationary hydrogen atom of mas s M emits a photon corresponding to the first line of Lyman series. If R is the Rydberg’s constant, the velocity that the atom acquires is
An electron jumps from the fourth orbit to the second orbit of hydrogen atom. Given: the Rydberg’s constant R = 10 5 cm − 1 . The frequency, in Hz, of the emitted radiation will be
The shortest wavelength of the Brackett series of a hydrogen-like atom (atomic number = z) is the same as the shortest wavelength of the Balmer series of hydrogen atom. The value of z is
If energy of K-shell electron is -40000 eV and if 60000 V potential is applied at Coolidge tube then which of the following X-ray will get form?
X-rays are produced by accelerating electrons by voltage V and let they strike a metal of atomic number Z. The highest frequency of X-rays produced is proportional to
Let λ α , λ β and λ α ′ denote the wavelengths of the X-rays of the K α , K β and L α in the characteristic X-rays for a metal
If the minimum wavelength obtained in an X-ray tube is 2.5 × 10 − 10 m , the operating potential of the tube will be
The wavelength K α X-rays produced by the X-ray tube is 0.76 Å atomic number of the node material of the tube is
The shortest wavelength produced in an X-ray tube operating at 0.5 million volt is
In X-ray tube, when the accelerating voltage V is halved, the difference between the wavelength of K α line and minimum wavelength of continuous X-ray spectrum
The frequency of emission line for any transition in positronium atom (consisting of a positron and an electron) is x times the frequency for the corresponding line in the case of H atom, where x is
Transitions between three energy levels in a particular atom give rise to three spectral lines of wavelengths, in increasing magnitudes, λ 1 , λ 2 , and λ 3 . Which one of the following equations correctly relates λ 1 , λ 2 , and λ 3 ?
The electron in a hydrogen atom makes a transition from n = n 1 to n = n 2 state. The time period of the electron in the initial state is eight times that in the final state. The possible values of n 1 and n 2 are
The wavelength of radiation required to excite the electron from the first orbit to the third orbit in a doubly ionized lithium atom will be
If potential energy between a proton and an electron is given | U | = k e 2 / 2 R 3 , where e is the charge of electron and R is the radius of atom, then radius of Bohr’s orbit is given by (h = Planck’s constant , k = constant)
An alpha particle of energy 5 MeV is scattered through 180° by a fixed uranium nucleus. The distance of the closest approach is of the order of
An electron with kinetic energy E eV collides with a hydrogen atom in the ground state. The collision is observed to be elastic for
The minimum kinetic energy required for ionization of a hydrogen atom is E 1 in case electron is collided with hydrogen atom. It is E 2 if the hydrogen ion is collided and E 3 when helium ion is collided. Then,
A hydrogen atom is in an excited state of principle quantum number n. It emits a photon of wavelength λ when it returns to the ground state. The value of n is
A neutron moving with a speed v makes a head-on collision with a hydrogen atom in ground state kept at rest. The minimum kinetic energy of the neutron for which inelastic collision will take place is (assume that mass of proton is nearly equal to the mass of neutron)
An electron in a Bohr orbit of hydrogen atom with the quantum number n 2 has an angular momentum 4.2176 × 10 − 34 kgm 2 s − 1 . If the electron drops from this level to the next lower level, the wavelength of this line is
A sample of hydrogen gas is excited by means of a monochromatic radiation. In the subsequent emission spectrum, 10 different wavelengths are obtained, all of which have energies greater than or equal to the energy of the absorbed radiation. The initial quantum number of the state (before absorbing radiation) is
A hydrogen like atom of atomic number Z is in an excited state of quantum number 2n. It can emit a maximum energy photon of 204 eV. If it makes a transition to quantum state n, & photon of energy 40.8 eV is emitted. The value of n is
If the series limit of Lymen series for Hydrogen atom is equal to the series limit of Balmer series for a hydrogen like atom, then what is the atomic number of this hydrogen like atom?
A sample of monatomic hydrogen gas contains 100 atoms and all the atoms are in nth excited state. As the atoms come down to the ground state following various transitions, they release a total energy of 4800 49 R c h (where 1 Rch = 13.6eV) . Find the value of N, where maximum possible number of photons emitted in the process is 7N x 100.
What is the distance of closest approach(in x10 -14 m) when a 5.0 MeV proton approaches a gold nucleus?
The innermost orbit of the hydrogen atom has a diameter of 1.06 Å . What is the diameter (in Å ) of the tenth orbit?
The total energy of the electron in the first excited state of hydrogen is – 3.4 eV. What is the kinetic energy of the electron (in eV) in this state?
Find the ratio of minimum to maximum wavelength of radiation emitted by electron in ground state of Bohr’s hydrogen atom.
In hydrogen-like atom (atomic number A is in a higher excited state of quantum number n. This excited atom can make a transition to first excited state by emitting photons of energies 10.20 eV and 17.00 eV respectively. Alternatively the atom from the same excited state can make a transition to the second excited state by successively emitting two photons of energies 4.25 eV and 5.95 eV respectively. Determine values of n (ionization energy of hydrogen atom = 13.6 eV).
A gas of hydrogen-like ions is prepared in such a way that ions are only in the ground state and the first excited state. A monochromatic light of wavelength 1218 Å is absorbed by the ions. The ions are lifted to higher excited states and emit radiation of six wavelength, some higher and some lower than the incident wavelength. Calculate the values of the minimum wavelengths (in Å ).
Determine the separation of the first line of the Balmer series (in Å ) in a spectrum of ordinary hydrogen and tritium (mass number 3). Take Rydberg’s constants = 10967800 m -1 .
A hydrogen atom moves with a velocity u and makes a head on inelastic collision with another stationary hydrogen atom. Both are in the ground state before collision. What is the minimum value of u (in x10 4 m/s ), if one of them is to be given a minimum excitation energy? The ionization energy is 13.6 eV. Mass of the hydrogen atom is 1.0078 x 1.66 x 10 -27 kg.
The electron, in a hydrogen atom, initially in a state of quantum number n 1 , makes a transition to a state whose excitation energy, with respect to the ground state, is 10.2eV. If the wavelength, associated with the photon emitted in this transition, is 487 .5 nm, find the value of the quantum number, n 1 of the electron in its initial state.
50% of X-rays obtained from a Coolidge tube pass through 0.3mm thick aluminum foil. If the potential difference between the target and the cathode is increased, then the fraction of X-rays passing through the same foil will be
The potential difference applied to an X-ray tube is V. The ratio of the de Broglie wavelength of electron to the minimum wavelength of X-ray is directly proportional to
In Bohr’s theory the potential energy of an electron at a position is K r 2 2 (where K is a positive constant); then the quantized energy of the electron in nth orbit is:
A cobalt (atomic no. = 27) target is bombarded with electrons, and the wavelengths of its characteristic X-ray spectrum are measured. A second weak characteristic spectrum is also found, due to an impurity in the target. The wavelengths of the K α lines are 225.0 pm (cobalt) and 100.0 pm (impurity). If the atomic number of the impurity is 10 N. The value of N is (take b = 1)
The wavelength of K α line from an element of atomic number 51 is λ . From another element the wavelength of K α line is 4 λ . What is the atomic number of the second element?
An X-ray tube is working at potential of 20 kV. The potential difference is decreased to 10 kV. It is found that the difference of the wavelength of K α X-ray and the most energetic continuous X-ray becomes 4 times the difference before the change of voltage. The atomic number of the target element is Take b=1 and 1 3.4 = 0.54
K α wavelength emitted by an atom of atomic number Z = 11 is λ ,. Find the atomic number for an atom that emits K α -radiation with wavelength 4 λ .
The potential difference across the Coolidge tube is 20 kV and 10 mA current flows through the voltage supply. Only 0.5% of the energy carried by the electrons striking the target is converted into X-rays. The power carried by X-ray beam (in W) is
The wavelength of K α , X-rays produced by an X-ray tube is 0.76 A o . The atomic number of the anode material of the tube is .
Which source is associated with a line emission spectrum?
The spectrum of light emitted by a glowing solid is
Band spectrum is obtained when the source emitting light is in the form of or Band spectrum is characteristic of
Band spectrum is produced by
The spectrum of iodine gas under white light will be
Continuous spectrum is not due to
The wavelength of emission line spectrum and absorption line spectrum of a substance are related as
From which source a continuous emission spectrum and a line absorption spectrum are simultaneously obtained
Line spectra are due to
Which of the following spectrum have all the frequencies from high to low frequency range
The spectrum obtained from an electric lamp or red hot heater is
The band spectra (characteristic of molecular species) is due to emission of radiation
In absorption spectrum of Na the missing wavelength (s) are
