Cut off potentials for a metal in photoelectric effect for light of wavelength l1, l2 and l3 is found to be V1, V2 and V3 volts if V1, V2 and V3 are in Arithmetic Progression and l1, l2 and l3 will bea)Arithmetic Progressionb)Geometric Progressionc)Harmonic Progressiond)NoneCorrect answer is option 'C'. Can you explain this answer?

Question

Answer

I think their is no sequence just like arithmetic progression so the correct option is c

Answer

We know that,
eV=(hc/λ)-w
V=(hc/eλ)-(w/e)
Arithmetic progression =>V₂=(V₁+V₂)/2
Now,
(hc/eλ₂)-w/e=1/2[(hc/eλ₁)-(w/e) +(hc/eλ₃) -(w/e)]
=>1/ λ₂=1/2[(1/ λ₁)+(1/λ₃)]
=>2/ λ₂=1/ λ₁ + 1/λ₃
Hence the correct answer is harmonic Progression.

Answer

Explanation:

When light of a certain wavelength falls on a metal surface, electrons are emitted from the metal surface. This phenomenon is called the photoelectric effect. The energy of the incident photons determines the kinetic energy of the emitted electrons.

The cut-off potential for a metal is the minimum potential difference required to stop the emission of electrons. It is directly proportional to the maximum kinetic energy of the emitted electrons.

Given that the cut-off potentials for the metal for light of wavelengths l1, l2, and l3 are V1, V2, and V3 volts respectively, and that V1, V2, and V3 are in arithmetic progression, we need to determine the relationship between the wavelengths l1, l2, and l3.

Relationship between cut-off potentials and wavelengths:

The kinetic energy of the emitted electrons can be given by the equation:

K.E. = h * c / λ - φ

where h is Planck's constant, c is the speed of light, λ is the wavelength of the incident light, and φ is the work function of the metal.

As the cut-off potential is directly proportional to the maximum kinetic energy, we can write:

V1 ∝ K.E.(l1)
V2 ∝ K.E.(l2)
V3 ∝ K.E.(l3)

Since V1, V2, and V3 are in arithmetic progression, we can write:

V2 - V1 = V3 - V2

This implies that the differences in the cut-off potentials are equal:

V2 - V1 = V3 - V2

Relationship between wavelengths:

To find the relationship between the wavelengths l1, l2, and l3, we can equate the kinetic energies:

K.E.(l1) = K.E.(l2) = K.E.(l3)

Using the equation for kinetic energy, we get:

h * c / l1 - φ = h * c / l2 - φ = h * c / l3 - φ

Simplifying the equation, we get:

c / l1 = c / l2 = c / l3

This implies that the wavelengths l1, l2, and l3 are in harmonic progression.

Therefore, option C (Harmonic Progression) is the correct answer.

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