AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

Positronium is a system consisting of an electron and its antiparticle a positron, bound together by their electrostatic attraction. Assume that both particles revolve about their common centre of mass. Mark the CORRECT options remaining in the framework of Bohr’s hydrogen atom model. Use $K_{e} - \frac{1}{4 π ε_{0}}, h = \frac{h}{2 π}$ and standard notations.

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

Radius of n^th orbit is $r_{n} = (\frac{ℏ^{2}}{m k_{e}^{2} e^{2}}) n^{2}$

Speed in n^th orbit is $u_{n} = (\frac{K_{e} e^{2}}{2 ℏ}) \frac{1}{n}$

Total energy of the bound state is $E_{n} = - \frac{m {(k_{e} e^{2})}^{2}}{4 ℏ^{2}} \frac{1}{n^{2}}$

The magnitudes of the energy levels are exactly one-half of the corresponding value of Bohr’s H-atom.

answer is B, C, D.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Force Equation

$\frac{k e^{2}}{{(2 r_{n})}^{2}} = \frac{m v_{n}^{2}}{r_{n}} \dots \dots \dots \dots \dots \dots \dots (1)$

From Quantization of angular momentum

$m v_{n} r_{n} + m v_{n} r_{n} = \frac{n h}{2 π} \Rightarrow 2 m v_{n} r_{n} = \frac{n h}{2 π} \dots \dots \dots \dots \dots \dots (2)$

Solving equation (1) & (2) we get

$\begin{array}{l} r_{n} = (\frac{ℏ^{2}}{m k e^{2}}) n^{2} \\ v_{n} = (\frac{k e^{2}}{2 h}) \frac{1}{n} \end{array}$

Total Energy $E_{n} = \frac{{(P E)}_{n}}{2}$

$E_{n} = \frac{- k e^{2}}{2 (2 r_{n})}$

Watch 3-min video & get full concept clarity

courses

No courses found

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Get Expert Academic Guidance – Connect with a Counselor Today!