Question:
The threshold wavelength for photoelectric effect from a copper surface with work functions 4.5 eV is
The threshold wavelength for photoelectric effect from a copper surface with work functions 4.5 eV is
Updated On: Jun 13, 2025
- 276nm
- 676nm
- 726nm
- 267nm
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The Correct Option is A
Solution and Explanation
To determine the threshold wavelength for the photoelectric effect from a copper surface with a work function of 4.5 eV, we must first convert the work function from electron volts to joules. The conversion factor is 1 eV = 1.602 × 10-19 J.
Work function, φ = 4.5 eV = 4.5 × 1.602 × 10-19 J = 7.209 × 10-19 J.
The energy of a photon is given by the equation E = hν, where h is Planck's constant (6.626 × 10-34 Js) and ν is the frequency of the photon. The relationship between the speed of light (c), frequency (ν), and wavelength (λ) is c = λν.
Combining these, we have E = hc/λ.
For the threshold wavelength, E = φ. Therefore:
φ = hc/λ
λ = hc/φ
Substitute the known values:
h = 6.626 × 10-34 Js,
c = 3 × 108 m/s,
φ = 7.209 × 10-19 J.
λ = (6.626 × 10-34 Js) × (3 × 108 m/s) / (7.209 × 10-19 J)
λ = 2.756 × 10-7 m = 275.6 nm.
Hence, the threshold wavelength is approximately 276 nm. Therefore, the correct answer is 276 nm.
Work function, φ = 4.5 eV = 4.5 × 1.602 × 10-19 J = 7.209 × 10-19 J.
The energy of a photon is given by the equation E = hν, where h is Planck's constant (6.626 × 10-34 Js) and ν is the frequency of the photon. The relationship between the speed of light (c), frequency (ν), and wavelength (λ) is c = λν.
Combining these, we have E = hc/λ.
For the threshold wavelength, E = φ. Therefore:
φ = hc/λ
λ = hc/φ
Substitute the known values:
h = 6.626 × 10-34 Js,
c = 3 × 108 m/s,
φ = 7.209 × 10-19 J.
λ = (6.626 × 10-34 Js) × (3 × 108 m/s) / (7.209 × 10-19 J)
λ = 2.756 × 10-7 m = 275.6 nm.
Hence, the threshold wavelength is approximately 276 nm. Therefore, the correct answer is 276 nm.
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