A particle of mass $200 MeV / c^{2}$ 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 (in eV) is $\frac{N}{4}$ . The value of N is_______ (Given the mass of the hydrogen atom to be 1 $GeV / c^{2}$ )

see full answer

Start JEE / NEET / Foundation preparation at rupees 99/day !!

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

answer is 51.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

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

Take Free Test

Detailed Solution

From linear momentum conservation, $L_{i} = L_{f}$
$mV + 0 = 0 + 5 mV' \Rightarrow V' = \frac{v}{5}$
Loss of KE $= {KE}_{i} - {KE}_{f} = \frac{1}{2} {mv}^{2} - \frac{1}{2} (5 m) {(\frac{v}{5})}^{2}$
$= \frac{1}{2} {mv}^{2} (1 - \frac{1}{5}) = \frac{4}{5} (\frac{{mv}^{2}}{2})$
$= \frac{4}{5} {KE}_{i} = 10.2 eV$
[ $∵$ Energy in first excited state of atom = 10.2 eV]
${KE}_{i} = 12.75 eV = \frac{N}{4} \Rightarrow N = 51$
The value of N = 51.

Watch 3-min video & get full concept clarity

tricks from toppers of Infinity Learn

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

🔥 Start Your JEE/NEET Prep at Just ₹1999 / month - Limited Offer! Check Now!

Get Expert Academic Guidance – Connect with a Counselor Today!

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET