Question

In case of photoelectric emission from certain metal, the cutoff frequency is \(ν\). If the radiation of frequency \(3ν\) is incident on the metal plate, the maximum possible velocity of the emitted electrons will be (\(m\) = mass of electron, \(h\) = Planck's constant)

• A. \(\sqrt{\frac{hν}{2m}}\)
• B. \(\sqrt{\frac{hν}{m}}\)
• C. \(2(\sqrt{\frac{hν}{m}})\)
• D. \(\sqrt{\frac{2hν}{m}}\)

Hint:

Use Einstein equation with the work function equal to h times the cutoff frequency.

Answer 1

The Correct Option is C

Step 1: Energy balance:
Incident energy $3h\nu$, energy needed to escape $h\nu$, left over for motion $2h\nu$.

Step 2: Speed:
$v = \sqrt{\frac{2 \times 2h\nu}{m}} = \sqrt{\frac{4h\nu}{m}} = 2\sqrt{\frac{h\nu}{m}}$.

Final Answer:
$v_{max} = 2\sqrt{\frac{h\nu}{m}}$, option (C). \[ \boxed{2\sqrt{\frac{h\nu}{m}}} \]