Light is incident on a metallic plate having work function 110 × 10⁻²⁰ J. If the produced photoelectrons have zero kinetic energy then the angular frequency of the incident light is ___

Light is incident on a metallic plate having work function 110 × 10⁻²⁰ J

Q. Light is incident on a metallic plate having work function $110 \times 10^{-20}\ \text{J}$. If the produced photoelectrons have zero kinetic energy then the angular frequency of the incident light is ____ rad/s. $(h = 6.63 \times 10^{-34}\ \text{J·s})$.

(A) $1.04 \times 10^{13}$

(B) $1.66 \times 10^{16}$

(D) $1.04 \times 10^{16}$

Correct Answer: $1.04 \times 10^{16}$

Explanation

According to Einstein’s photoelectric equation,

$$ h\nu = \phi + K_{\text{max}} $$

Given that the kinetic energy of photoelectrons is zero,

$$ h\nu = \phi $$

Angular frequency $\omega$ is related to frequency by

$$ \omega = 2\pi\nu $$

Substituting $\nu = \dfrac{\phi}{h}$,

$$ \omega = 2\pi \frac{\phi}{h} $$

Given,

$$ \phi = 110 \times 10^{-20}\ \text{J}, \quad h = 6.63 \times 10^{-34}\ \text{J·s} $$

$$ \omega = 2\pi \times \frac{110 \times 10^{-20}}{6.63 \times 10^{-34}} $$

$$ \omega \approx 1.04 \times 10^{16}\ \text{rad/s} $$

Hence, the angular frequency of the incident light is

$1.04 \times 10^{16}\ \text{rad/s}$.

Explanation

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