Q28. The wavelength of light from the spectral emission line of sodium is 662 nm. The kinetic energy

Q: What is the correct answer for CUET UG Physics Q28?

The correct answer is a. The de Broglie wavelength (λ) of a particle is related to its momentum (p) by λ = h/p. The kinetic energy (K) of a non-relativistic particle is K = p²/(2m). Combining these, we can express kinetic energy in terms of wavelength: p = h/λ, so K = (h/λ)² / (2m) = h² / (2mλ²). Given λ = 662 nm = 662 × 10⁻⁹ m, Planck's constant h = 6.62 × 10⁻³⁴ J·s, and mass of electron m_e = 9 × 10⁻³¹ kg. Substitute th

Q: Q28. The wavelength of light from the spectral emission line of sodium is 662 nm. The kinetic energy at which an electron would have same de-Broglie wavelength would be: (h = 6.62 x 10⁻³⁴ J-s, me = 9…

The correct answer is a. The de Broglie wavelength (λ) of a particle is related to its momentum (p) by λ = h/p. The kinetic energy (K) of a non-relativistic particle is K = p²/(2m). Combining these, we can express kinetic energy in terms of wavelength: p = h/λ, so K = (h/λ)² / (2m) = h² / (2mλ²). Given λ = 662 nm = 662 × 10⁻⁹ m, Planck's constant h = 6.62 × 10⁻³⁴ J·s, and mass of electron m_e = 9 × 10⁻³¹ kg. Substitute th

Q: What are the options for this CUET UG Physics question?

A. 5.5 x 10⁻²⁵ J · B. 5.5 x 10⁻²⁴ J · C. 18 x 10⁻²³ J · D. 4.5 x 10⁻²² J

Question

Q28. The wavelength of light from the spectral emission line of sodium is 662 nm. The kinetic energy at which an electron would have same de-Broglie wavelength would be: (h = 6.62 x 10⁻³⁴ J-s, me = 9 x 10⁻³¹ kg)

FirstInTest · Accepted Answer

The de Broglie wavelength (λ) of a particle is related to its momentum (p) by λ = h/p. The kinetic energy (K) of a non-relativistic particle is K = p²/(2m). Combining these, we can express kinetic energy in terms of wavelength: p = h/λ, so K = (h/λ)² / (2m) = h² / (2mλ²). Given λ = 662 nm = 662 × 10⁻⁹ m, Planck's constant h = 6.62 × 10⁻³⁴ J·s, and mass of electron m_e = 9 × 10⁻³¹ kg. Substitute these values into the formula: K = (6.62 × 10⁻³⁴)² / [2 × (9 × 10⁻³¹) × (662 × 10⁻⁹)²]. K = (6.62)² × 10⁻⁶⁸ / [18 × 10⁻³¹ × (6.62 × 10² × 10⁻⁹)²] = (6.62)² × 10⁻⁶⁸ / [18 × 10⁻³¹ × (6.62)² × 10⁻¹⁴]. Cancelling (6.62)²: K = 10⁻⁶⁸ / (18 × 10⁻⁴⁵) = (1/18) × 10⁻²³ J ≈ 0.0555 × 10⁻²³ J = 5.55 × 10⁻²⁵ J. This value matches option (a).

Answer

5.5 x 10⁻²⁵ J

Answer

5.5 x 10⁻²⁴ J

Answer

18 x 10⁻²³ J

Answer

4.5 x 10⁻²² J

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