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Concepts Of Physics MCQ Edition [Volume 2]
Exam
Concepts Of Physics MCQ Edition [Volume 2]
Subject
Physics
Chapter
Bohr's Model and Physics of the Atom

Concepts Of Physics MCQ Edition [Volume 2] · Physics · Bohr's Model and Physics of the Atom

Calculate the Rydberg constant by substituting the values of the...

Calculate the Rydberg constant by substituting the values of the fundamental constants into its expression.

Options

  1. A1.097×105 m−11.097 \times 10^5 \text{ m}^{-1}
  2. B1.097×107 m−11.097 \times 10^7 \text{ m}^{-1}
  3. C1.097×109 m−11.097 \times 10^9 \text{ m}^{-1}
  4. D1.097×1011 m−11.097 \times 10^{11} \text{ m}^{-1}

Correct answer

B. 1.097×107 m−11.097 \times 10^7 \text{ m}^{-1}

Step-by-step solution

The expression for the Rydberg constant is given by:

R=me48ϵ02h3cR = \dfrac{m e^4}{8 \epsilon_0^2 h^3 c}

Substituting the values of the fundamental constants:
m=9.1×10−31 kgm = 9.1 \times 10^{-31} \text{ kg}
e=1.6×10−19 Ce = 1.6 \times 10^{-19} \text{ C}
ϵ0=8.85×10−12 F m−1\epsilon_0 = 8.85 \times 10^{-12} \text{ F m}^{-1}
h=6.63×10−34 J sh = 6.63 \times 10^{-34} \text{ J s}
c=3×108 m s−1c = 3 \times 10^8 \text{ m s}^{-1}

R=(9.1×10−31)×(1.6×10−19)48×(8.85×10−12)2×(6.63×10−34)3×(3×108)R = \dfrac{(9.1 \times 10^{-31}) \times (1.6 \times 10^{-19})^4}{8 \times (8.85 \times 10^{-12})^2 \times (6.63 \times 10^{-34})^3 \times (3 \times 10^8)}

R=1.097×107 m−1R = 1.097 \times 10^7 \text{ m}^{-1}
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