When light radiation wavelength (lambda) is incidented photoelectric effect take place, now wavelength of light becomes 5 (lambda) and maximum kinetics of emitted photo e- becomes 1/3th of initial.find threshold wavelength.?

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5 lyamada

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Introduction:
The photoelectric effect is the phenomenon in which electrons are emitted from a material when light of a certain frequency, known as the threshold frequency, is incident on it. The energy of the incident photons must be greater than or equal to the work function of the material for electrons to be emitted.

Given:
- Initial wavelength of light: λ
- Final wavelength of light: 5λ
- Maximum kinetic energy of emitted photoelectrons is 1/3 of the initial value.

Calculating the threshold wavelength:
To find the threshold wavelength, we can use the concept of the relationship between the energy of a photon and its wavelength. The energy of a photon is given by the equation E = hc/λ, where h is Planck's constant (6.626 x 10^-34 J s), c is the speed of light (3 x 10^8 m/s), and λ is the wavelength of light.

Step 1: Finding the initial energy of the photons:
The initial energy of the photons can be calculated using the given initial wavelength (λ). Let's denote this energy as E_initial.

E_initial = hc/λ

Step 2: Finding the final energy of the photons:
The final energy of the photons can be calculated using the given final wavelength (5λ). Let's denote this energy as E_final.

E_final = hc/(5λ)

Step 3: Relationship between energy and maximum kinetic energy:
According to the photoelectric effect, the maximum kinetic energy (KEmax) of the emitted photoelectrons is given by the equation:

KEmax = E_initial - Work function

Since the maximum kinetic energy is 1/3 of the initial value, we can write:

KEmax = (1/3) * E_initial

Step 4: Relationship between energy and threshold wavelength:
The threshold wavelength (λ_threshold) can be calculated using the equation:

E_threshold = hc/λ_threshold

Step 5: Solving for the threshold wavelength:
Using the relationships mentioned above, we can equate the energies to find the threshold wavelength.

(1/3) * E_initial = E_threshold

(1/3) * hc/λ = hc/λ_threshold

Simplifying the equation:

λ_threshold = 3λ

Conclusion:
The threshold wavelength is 3 times the initial wavelength (λ_threshold = 3λ).

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