Q.

In a hypothetical atom, a negatively charged particle having a charge of magnitude 3e and mass 3m revolves around a proton. Here, e is the electronic charge and m is the electronic mass. Mass of proton may be assumed to be much larger than that of the negatively charged particle, thus the proton is at rest. This “atom” obeys Bohr’s postulate of quantization of angular momentum, that is mvr=nh2π  . It is given that for the first Bohr orbit of hydrogen atom: radius of orbit is  r0  speed of electron is v0  , and total energy is  -E0.

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a

 Radius of first orbit of this atom is  r09.

b

Radius of first orbit of hypothetical atom is r027 .

c

Speed of the revolving particle in the hypothetical atom is 9v0  in the first Bohr orbit.

d

Speed of the revolving particle in the hypothetical atom is 3v0  in the first Bohr orbit.

answer is B, C.

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Detailed Solution

 If mass of revolving particle is m, and charge q, charge at nucleus Q.
 mvr=nh2π

mv2r=k(Q)qr2
Equating  v2
 n2h2π2m2r2=kQqmrr=n2h2π2n2mkQq
Energy of nth orbit
En=k+U=12mv2-kQqr
=  12kQqr=12mkQq2h2π2n2
For hydrogen atom
Q = e, q = e, m = me , Q = e, q = e, m =  me
For hypothetical atom
Q = e, q = 3e, m = 3 me
Radius of first orbit of this atom
  
r01=r09

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