JEE Physics 2023 Question with Solution

Given: Threshold wavelength is $\lambda_{\text{threshold}} = 5500 \, \text{Å}$.

Find: Which source can cause photoelectric emission.

For photoelectric emission, radiation must satisfy

$$\lambda < \lambda_{\text{threshold}}$$

Infra-red radiation has wavelength greater than the threshold wavelength, so it cannot eject photoelectrons.

Ultra-violet radiation has wavelength less than the threshold wavelength, so it can eject photoelectrons.

Therefore, both ultra-violet lamps listed in the statement, C and D, will cause emission. The correct option is D.

Given: Infra-red and ultra-violet sources are to be compared with the threshold wavelength.

Find: Which radiation has wavelength below the threshold.

A quick comparison is:

• Infra-red has comparatively large wavelength.
• Ultra-violet has comparatively small wavelength.

Using typical ranges,

$$\lambda_{\text{IR}} \gtrsim 700 \, \text{nm}$$

and

$$\lambda_{\text{UV}} \approx 100 \text{ to } 400 \, \text{nm}$$

Also,

$$5500 \, \text{Å} = 550 \, \text{nm}$$

So only ultra-violet radiation satisfies the condition for emission. Hence the emitting sources are C and D, so the correct option is D.