Question:
The work function of Mg, Cu, Ag, Li are \(3.7, 4.8, 4.3, 2.5\,\text{eV}\) respectively. A wavelength of \(300\,\text{nm}\) light is shined on them. The metals which undergo photoelectric effect are
The work function of Mg, Cu, Ag, Li are \(3.7, 4.8, 4.3, 2.5\,\text{eV}\) respectively. A wavelength of \(300\,\text{nm}\) light is shined on them. The metals which undergo photoelectric effect are
Show Hint
Use the shortcut formula:
\[
E(\text{eV}) = \frac{1240}{\lambda(\text{nm})}
\]
If photon energy exceeds work function, photoelectric emission occurs immediately.
Updated On: Jun 17, 2026
- Mg, Cu
- Cu, Ag
- Ag, Li
- Mg, Li
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The Correct Option is D
Solution and Explanation
Concept:
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 photon energy is calculated using:
\[
E = \frac{hc}{\lambda}
\]
A useful shortcut formula is:
\[
E(\text{eV}) = \frac{1240}{\lambda(\text{nm})}
\]
If:
\[
E \geq \phi
\]
then photoelectric emission occurs.
Otherwise, electrons are not emitted.
Step 1: Calculate energy of incident radiation. Given: \[ \lambda = 300\,\text{nm} \] Using: \[ E = \frac{1240}{300} \] \[ E = 4.13\,\text{eV} \] Thus, incident photon energy is: \[ E = 4.13\,\text{eV} \]
Step 2: Compare photon energy with work function of each metal. For Mg: \[ \phi = 3.7\,\text{eV} \] Since, \[ 4.13 > 3.7 \] Therefore, Mg shows photoelectric effect. For Cu: \[ \phi = 4.8\,\text{eV} \] Since, \[ 4.13 < 4.8 \] Therefore, Cu does not show photoelectric effect. For Ag: \[ \phi = 4.3\,\text{eV} \] Since, \[ 4.13 < 4.3 \] Therefore, Ag does not show photoelectric effect. For Li: \[ \phi = 2.5\,\text{eV} \] Since, \[ 4.13 > 2.5 \] Therefore, Li shows photoelectric effect.
Step 3: Identify the correct metals. The metals which undergo photoelectric effect are: \[ \boxed{\text{Mg and Li}} \] Hence, the correct option is: \[ \boxed{(D)} \]
Step 1: Calculate energy of incident radiation. Given: \[ \lambda = 300\,\text{nm} \] Using: \[ E = \frac{1240}{300} \] \[ E = 4.13\,\text{eV} \] Thus, incident photon energy is: \[ E = 4.13\,\text{eV} \]
Step 2: Compare photon energy with work function of each metal. For Mg: \[ \phi = 3.7\,\text{eV} \] Since, \[ 4.13 > 3.7 \] Therefore, Mg shows photoelectric effect. For Cu: \[ \phi = 4.8\,\text{eV} \] Since, \[ 4.13 < 4.8 \] Therefore, Cu does not show photoelectric effect. For Ag: \[ \phi = 4.3\,\text{eV} \] Since, \[ 4.13 < 4.3 \] Therefore, Ag does not show photoelectric effect. For Li: \[ \phi = 2.5\,\text{eV} \] Since, \[ 4.13 > 2.5 \] Therefore, Li shows photoelectric effect.
Step 3: Identify the correct metals. The metals which undergo photoelectric effect are: \[ \boxed{\text{Mg and Li}} \] Hence, the correct option is: \[ \boxed{(D)} \]
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