Problem 16 - Master Resource Book in JEE Main Physics

Question

Which one of the following statements regarding photo-emission of electrons is correct? (a) Kinetic energy of electrons increases with the intensity of incident light (b) Electrons are emitted when the wavelength of the incident light is above a certain threshold wavelength (c) Photoelectric emission is instantaneous with the incidence of light (d) Photo electrons are emitted whenever a gas is irradiated with ultraviolet light

Step-by-Step Solution

Answer

(c) Photoelectric emission is instantaneous with the incidence of light.

Step 1: Understanding the Photoelectric Effect

The photoelectric effect is a phenomenon where electrons are emitted from a material when it absorbs light. The ejection of electrons depends on the frequency of the incident light, not the intensity. Intensity affects the number of electrons but doesn't change their kinetic energy.

Step 2: Evaluate Each Option

(a) The kinetic energy of electrons depends on the frequency, not intensity, of the light. (b) Emission occurs when the frequency is above the threshold (equivalent to the wavelength being below a certain threshold). (c) Emission is generally immediate, without measurable delay. (d) UV light can cause emission only if the light has sufficient energy (frequency above the threshold).

Step 3: Analysis of Options

(a) Incorrect - Intensity affects the number of emitted electrons, not their kinetic energy. (b) Misleading - Below the threshold wavelength (above the threshold frequency), electrons are emitted. (c) Correct - Photoelectric effect is usually instantaneous. (d) Incorrect - Emission requires UV light to be above threshold frequency.

Step 4: Conclusion

Considering all options and understanding the photoelectric effect, the correct statement is about the immediacy of photoelectron emission upon light incidence.

Key Concepts

Threshold Frequency

When discussing the photoelectric effect, the threshold frequency is a fundamental concept. It is the minimum frequency of incident light required to eject electrons from a material. This frequency is specific to each material and is related to its work function, which is the energy needed to remove an electron from the surface. The relationship between frequency and wavelength is given by the equation \[ c = \lambda u \]where \(c\) is the speed of light, \(\lambda\) is the wavelength, and \(u\) is the frequency. - If the incident light's frequency is below this threshold, electrons are not emitted, regardless of the light intensity. - When frequency is above the threshold, electrons can be emitted, indicating the photoelectric effect has occurred. This illustrates that to achieve electron emission, adjusting frequency rather than intensity is crucial. An understanding of frequency and threshold helps to explain why certain light sources, like ultraviolet light, can cause photoemission.

Kinetic Energy of Electrons

The kinetic energy of electrons emitted in the photoelectric effect is a critical concept to understand. When electrons are emitted, they possess kinetic energy, which depends on the frequency of the incident light above the threshold frequency. The equation used for calculating this energy is known as the photoelectric equation:\[ KE = h(u - u_0) \]where \(KE\) is the kinetic energy of the emitted electrons, \(h\) is Planck's constant, \(u\) is the frequency of the incident light, and \(u_0\) is the threshold frequency. - Only light with a frequency higher than the threshold frequency contributes to increasing the kinetic energy of electrons. - It is essential to note that increasing the intensity of the light only increases the number of electrons emitted and not their energy.Understanding this equation not only highlights the dependency on frequency over intensity but also helps in realizing the conditions under which electrons can be emitted with specific kinetic energies.

Intensity of Light

While studying the photoelectric effect, the intensity of light plays a significant role, albeit differently from frequency. Intensity refers to the amount of energy the light wave carries per second, often considered as the brightness of the light source. - Increasing the light intensity results in more photons hitting the surface per second. - As a result, more electrons are emitted if the light's frequency is above the threshold frequency. However, intensity does not affect the energy of the emitted electrons; it only influences the number. The photoelectric effect thus uniquely illustrates that while intensity impacts the quantity of emitted electrons, it does not alter their kinetic energy. This distinction is vital for understanding the behavior of light and matter in quantum mechanics.