Question

A hydrogen atom moving with velocity $u$ collides, in-elastically with another hydrogen atom at rest. Both the atoms are in the ground state before collioson. The minimum value of $u$, so that one of the atoms get excited, will be

• A. 3.12 x 10${}^6$ m/s
• B. 9.36 x 10${}^5$ m/s
• C. 6.24 x 10${}^4$ m/s
• D. 5 x 10${}^3$ m/s

Answer 1

The correct option is C 6.24 x 10${}^4$ m/s

Energy needed to excite at least one hydrogen atom is $10.2eV$, which is $1.63\times {10}^{-18}J$
K.E needed is double the energy.
$\frac{1}{2}m{v}^2=2(1.63\times {10}^{-18}J)$
$\Rightarrow v={\left(\frac{4(1.63\times {10}^{-18}J)}{1.67\times {10}^{-27}}\right)}^{\frac{1}{2}}=6.2\times {10}^4$

Therefore, minimum value of '$u$' is $6.2\times {10}^{4}m/s$