Question

Light from a discharge tube containing hydrogen atoms falls on the surface of a piece of sodium. The kinetic energy of the fastest photoelectrons emitted from sodium is $0.73eV$. The work function for sodium is $1.82eV$. The rocoil speed of emitting atom assuming it to be at rest before ionisation is $($Ionisation potential of hydrogen is $13.6eV)$.

• A. $0.18m{s}^{-1}$
• B. $1.80m{s}^{-1}$
• C. $8.10m{s}^{-1}$
• D. $0.81m{s}^{-1}$

Answer 1

Answer: (D)

$0.81m{s}^{-1}$

Momentum of hydrogen atom $=$ momentum of emitted photon
i.e. $mv=\frac{E}{c}$
$v=\frac{E}{mv}=\frac{(0.73+1.82)1.6\times {10}^{-19}}{1.67\times {10}^{-27}\times 3\times {10}^8}=0.81m{s}^{-1}$