A neutrons beam, in which each neutron has same Kinetic energy , is passed through a sample of hydrogen like gas (but not hydrogen) in ground state and at rest . Due to collision of neutrons with the ions of the gas, ions are excited and then they emit photons . Six spectral lines arer obtained in which one of the lines is of wavelength `(6200//51) nm` ltbr. what is the minimum possible value of kinetic energy of the neutrons for this possible . The mass of neutron and protons can be assumed to be nearly same . Use `hc=12400`

Options

A. `10.5eV`
B. `63.75eV`
C. `6.9eV`
D. `8.9eV`

Answer

B

Explanation

Let `u` be the speed of neurtron before collision
` (##NAR_PHY_XII_V05_C02_E01_317_S01.png" width="80%">
At end of the deformation phase (when the kinetic energy of (neutron +He^(+) system is least) ` (## NAR_PHY_XII_V05_C02_E01_317_S02.png" width="80%">
where `u_(cm)` is velocity of centre of mass . From conservation of momentum `u_(cm)=("mu")/(m+4m)=u/5`
The loss of Kinetic energy =`1/2"mu"^(2)-1/2m(u/5)^(2)-1/2 4m(u/5)^(2)=4/5(1/2"mu"^(2))`
If `K` is the Kinetic of neutron then the maximum loss in `K.E` of system is`(4K)/5 this excites the electron from `n=1` to `n=4`
4/5K=`51eV` or K=`(51xx5)/4=63.75eV
` K_(min)`=63.75eV`