Modern Physics 1 Question 25

22. Imagine an atom made up of proton and a hypothetical particle of double the mass of the electron but having the same charge as the electron. Apply the Bohr atom 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

(2000,2M)

(a) 9/5R

(b) 36/5R

(c) 18/5R

(d) 4/R

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Solution:

  1. In hydrogen atom, En=Rhcn2. Also, Enm where, m is the mass of the electron.

Here, the electron has been replaced by a particle whose mass is double of an electron. Therefore, for this hypothetical atom energy in nth  orbit will be given by

En=2Rhcn2

The longest wavelength λmax (or minimum energy) photon will correspond to the transition of particle from n=3 to n=2.

hcλmax=E3E2=2Rhc122132

This gives, λmax=18/5R



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