Problem 78 - Master Resource Book in JEE Main Physics

Question

Directions This question contain statement I and statement II. Of the four choices given after the statements, choice the one that best describes the two statements: (a) Statement 1 is true, Statement 11 is true; Statement 11 is the correct explanation of Statement 1 (b) Statement 1 is true, Statement 11 is true; Statement 11 is not the correct explanation of Statement 1 (c) Statement 1 is false, Statement 11 is true (d) Statement 1 is true, Statement \(\mathrm{ll}\) is false Statement I When ultraviolet light is incident on a photocell, its stopping potential is \(V_{0}\) and the maximum kinetic energy of the photoelectrons is \(K_{\max } .\) When the ultraviolet light is replaced by X-rays, both \(V_{0}\) and \(K_{\max }\) increase. Statement II Photoelectrons are emitted with speeds ranging from zero to a maximum value because of the range of frequencies present in the incident light.

Step-by-Step Solution

Answer

(b): Both statements are true, but Statement II is not the correct explanation of Statement I.

Step 1: Analyze Statement I

Statement I claims that when ultraviolet light is replaced by X-rays in a photocell, the stopping potential \(V_0\) and the maximum kinetic energy of the photoelectrons \(K_{\max}\) increase. This is true because X-rays have a higher frequency than ultraviolet light, which results in higher energy photons according to the equation \(E = hu\). Thus, the stopping potential and kinetic energy increase when higher energy X-rays are used.

Step 2: Analyze Statement II

Statement II states that photoelectrons are emitted with speeds ranging from zero to a maximum because of the range of frequencies in the incident light. This statement is true because the range of frequencies (and thus energies) of the incident light can result in photoelectrons being emitted with different kinetic energies.

Step 3: Evaluate the Explanation

We need to determine if Statement II explains Statement I. The increase in \(V_0\) and \(K_{\max}\) with X-rays instead of ultraviolet light is caused by higher frequency (and energy) of X-rays, not because of a range of frequencies. While Statement II describes a true phenomenon, it does not explain the cause of what is described in Statement I.

Step 4: Choose the Correct Option

Since both statements are true, but Statement II does not explain Statement I, the best choice is (b): Statement 1 is true, Statement 11 is true; Statement 11 is not the correct explanation of Statement 1.

Key Concepts

Photocells

Photocells, often known as photoelectric cells, are remarkable devices that convert light energy into electrical energy using the photoelectric effect. When light strikes the surface of a photocell, it causes the emission of electrons, which can result in an electric current. This phenomenon is the basis of the photoelectric effect. Photocells are integral components in various applications, including light meters, solar panels, and night vision equipment.

Understanding how different types of light affect photocells is crucial. For instance, when ultraviolet light hits a photocell, it emits photoelectrons with a specific range of kinetic energies. Replacing ultraviolet light with X-rays, which have higher frequencies, results in photoelectrons with even more energy. This behavior is critical to the operation of many scientific and industrial devices.

• Conversion of light to electrical energy
• Application in smart lighting and automation
• Key player in the solar energy sector

X-rays

X-rays are a form of electromagnetic radiation with very high energy and short wavelengths. They are known for their ability to penetrate various materials, which makes them incredibly useful in medical imaging, such as X-ray scans and security systems.

When it comes to photocells, X-rays can induce the emission of photoelectrons at higher energy levels than ultraviolet light. This is because the energy of photons is directly proportional to their frequency, following the equation \(E = h u\), where \(E\) is the energy, \(h\) is Planck's constant, and \(u\) is the frequency. Thus, the high frequency of X-rays corresponds to higher energy photons.

• High penetration capability in materials
• Utilized in medical diagnostics and security
• Higher frequencies lead to increased photoelectron energy

Ultraviolet Light

Ultraviolet (UV) light is a type of electromagnetic radiation that is part of the light spectrum just beyond visible light, with wavelengths shorter than visible light but longer than X-rays. It is known for its role in causing skin tanning and facilitating the production of Vitamin D in the human body.

In the context of the photoelectric effect, ultraviolet light can eject electrons from the surface of a photocell, producing photoelectrons with moderate kinetic energies. It is these stored electron energies that are harnessed in devices like photocells to generate electric current. With a lower frequency than X-rays, UV light leads to the emission of lower energy electrons. This characteristic makes UV light a critical factor in the design and use of various technologies that utilize photoelectric properties.

• Role in producing Vitamin D and causing suntan
• Moderate energy affecting photoelectric devices
• Shorter than visible light, yet longer than X-rays