Question 285: Dual Nature of Matter and Radiation

Question

Light of wavelength ' $\lambda$ ' falls on a metal having work function $\frac{\mathrm{hc}}{\lambda_0}$. Photoelectric effect will take place only if ( $\lambda_0$ is the threshold wavelength)

Accepted Answer

The photoelectric effect occurs only when the energy of the incident photon is
greater than or equal to
the work function of the metal.
The energy of the incident photon of wavelength $\lambda$ is:
$$ E = \frac{hc}{\lambda} $$
The work function ($\phi$) is given as:
$$ \phi = \frac{hc}{\lambda_0} $$
For photoelectric emission:
$$ E \geq \phi $$
So,
$$ \frac{hc}{\lambda} \geq \frac{hc}{\lambda_0} $$
Divide both sides by $hc$:
$$ \frac{1}{\lambda} \geq \frac{1}{\lambda_0} $$
Taking reciprocal (and reversing the inequality since reciprocals of positive numbers reverse the inequality sign):
$$ \lambda \leq \lambda_0 $$
Correct option:
Option C: $\lambda \leq \lambda_0$

Answer

$\lambda \geq \lambda_0$

Answer

$\lambda \geq 2 \lambda_0$

Answer

$\lambda \leq \lambda_0$

Answer

$\lambda=4 \lambda_0$

Dual Nature of Matter and Radiation

Light of wavelength ' \lambda ' falls on a metal having work function \frac{\mathrm{hc}}{\lambda_0}. Photoelectric effect will take place only if ( \lambda_0 is the threshold wavelength)

Choose the correct answer: