Q17. A particle moves three times as fast as an electron. The ratio of the de Broglie wavelength of

Q: What is the correct answer for CUET UG Physics Q17?

The correct answer is a. The de Broglie wavelength (λ) of a particle is given by the formula λ = h/p = h/(mv), where h is Planck's constant, m is the mass of the particle, and v is its velocity. Let the particle be denoted by 'p' and the electron by 'e'. We are given that v_p = 3v_e and λ_p / λ_e = 1.813 × 10⁻⁴. Using the de Broglie relation for both: λ_p = h / (m_p v_p) and λ_e = h / (m_e v_e). Taking the ratio of wavele

Q: Q17. A particle moves three times as fast as an electron. The ratio of the de Broglie wavelength of the particle to that of the electron is 1.813 x 10-4. The mass of the particle is: (a) 1.67 x 10-27…

The correct answer is a. The de Broglie wavelength (λ) of a particle is given by the formula λ = h/p = h/(mv), where h is Planck's constant, m is the mass of the particle, and v is its velocity. Let the particle be denoted by 'p' and the electron by 'e'. We are given that v_p = 3v_e and λ_p / λ_e = 1.813 × 10⁻⁴. Using the de Broglie relation for both: λ_p = h / (m_p v_p) and λ_e = h / (m_e v_e). Taking the ratio of wavele

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

A. 1.67 x 10-27 kg · B. 1.675 x 10-31 kg · C. 1.675 x 10-29 kg · D. 1.675 x 10-30 kg

Question

Q17. A particle moves three times as fast as an electron. The ratio of the de Broglie wavelength of the particle to that of the electron is 1.813 x 10-4. The mass of the particle is:
(a) 1.67 x 10-27 kg
(b) 1.675 x 10-31 kg
(c) 1.675 x 10-29 kg
(d) 1.675 x 10-30 kg

FirstInTest · Accepted Answer

The de Broglie wavelength (λ) of a particle is given by the formula λ = h/p = h/(mv), where h is Planck's constant, m is the mass of the particle, and v is its velocity. Let the particle be denoted by 'p' and the electron by 'e'. We are given that v_p = 3v_e and λ_p / λ_e = 1.813 × 10⁻⁴. Using the de Broglie relation for both: λ_p = h / (m_p v_p) and λ_e = h / (m_e v_e). Taking the ratio of wavelengths: λ_p / λ_e = (h / (m_p v_p)) / (h / (m_e v_e)) = (m_e v_e) / (m_p v_p). Substitute the given values: 1.813 × 10⁻⁴ = (m_e v_e) / (m_p * 3v_e) = m_e / (3m_p). Rearranging to solve for m_p: m_p = m_e / (3 * 1.813 × 10⁻⁴). Using the mass of an electron m_e ≈ 9.11 × 10⁻³¹ kg: m_p = (9.11 × 10⁻³¹ kg) / (5.439 × 10⁻⁴) ≈ 1.675 × 10⁻²⁷ kg. This value is approximately equal to the mass of a proton or neutron. Option (a) is 1.67 × 10⁻²⁷ kg, which is the closest value. Options (b), (c), and (d) are incorrect values, with different magnitudes typical for electrons or other particles.

Answer

1.67 x 10-27 kg

Answer

1.675 x 10-31 kg

Answer

1.675 x 10-29 kg

Answer

1.675 x 10-30 kg

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