Q34. The wavelength of radiation emitted, when He⁺ makes a transition from the state n = 3 to the st

Q: What is the correct answer for CUET UG Physics Q34?

The correct answer is B. The wavelength (λ) of radiation emitted during an electron transition in a hydrogen-like atom is given by the Rydberg formula: 1/λ = R Z² (1/n_f² - 1/n_i²), where R is the Rydberg constant, Z is the atomic number, n_i is the initial principal quantum number, and n_f is the final principal quantum number. Given: R = 1.097 x 10⁷ m⁻¹. For He⁺ (Helium ion), Z = 2. The transition is from n_i = 3 to n_

Q: Q34. The wavelength of radiation emitted, when He⁺ makes a transition from the state n = 3 to the state n = 2 will be: (Take Rydberg constant R - 1.097 x 10⁷ m⁻¹) (a) 1.641 nm (b) 164.1 nm (c) 16.41…

The correct answer is B. The wavelength (λ) of radiation emitted during an electron transition in a hydrogen-like atom is given by the Rydberg formula: 1/λ = R Z² (1/n_f² - 1/n_i²), where R is the Rydberg constant, Z is the atomic number, n_i is the initial principal quantum number, and n_f is the final principal quantum number. Given: R = 1.097 x 10⁷ m⁻¹. For He⁺ (Helium ion), Z = 2. The transition is from n_i = 3 to n_

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

A. 1.641 nm · B. 164.1 nm · C. 16.41 um · D. 1641 nm

Question

Q34. The wavelength of radiation emitted, when He⁺ makes a transition from the state n = 3 to the state n = 2 will be:
(Take Rydberg constant R - 1.097 x 10⁷ m⁻¹)
(a) 1.641 nm
(b) 164.1 nm
(c) 16.41 um
(d) 1641 nm

FirstInTest · Accepted Answer

The wavelength (λ) of radiation emitted during an electron transition in a hydrogen-like atom is given by the Rydberg formula: 1/λ = R Z² (1/n_f² - 1/n_i²), where R is the Rydberg constant, Z is the atomic number, n_i is the initial principal quantum number, and n_f is the final principal quantum number. 
Given: R = 1.097 x 10⁷ m⁻¹. For He⁺ (Helium ion), Z = 2. The transition is from n_i = 3 to n_f = 2. 
Substitute the values into the formula: 
1/λ = (1.097 x 10⁷ m⁻¹) * (2²) * (1/2² - 1/3²) 
1/λ = (1.097 x 10⁷) * 4 * (1/4 - 1/9) 
1/λ = (1.097 x 10⁷) * 4 * ((9 - 4) / 36) 
1/λ = (1.097 x 10⁷) * 4 * (5/36) 
1/λ = (1.097 x 10⁷) * (5/9) 
1/λ = 0.60944 x 10⁷ m⁻¹ 
Now, calculate λ: λ = 1 / (0.60944 x 10⁷ m⁻¹) = 1.64096 x 10⁻⁷ m. 
Converting to nanometers (1 nm = 10⁻⁹ m): λ = 164.096 x 10⁻⁹ m = 164.096 nm. 
Rounding to one decimal place, λ ≈ 164.1 nm. This matches option (b).

Answer

1.641 nm

Answer

164.1 nm

Answer

16.41 um

Answer

1641 nm

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