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QPages 384-386: Q4: HC Verma: Concepts of Physics - Volume 2 Bohr's Model and Physics of the Atom Pages 384-386: Q4 Solution: Evaluate Rydberg constant by putting the values of the…

⚠️ Common Exam Traps & Conceptual Pitfalls

When raising constants to powers, multiply exponents correctly; for example $(1.6 imes10^{-19})^4=1.6^4 imes10^{-76}$, not $10^{-19}$. Likewise $epsilon_0$ must be squared and $h$ cubed. A single misplaced exponent changes the result by many orders of magnitude, leading to an incorrect Rydberg constant.

Evaluate Rydberg constant by putting the values of the fundamental constants in its expression.

Step-by-Step Verified Solution

**Answer:** R=1.097×107R = 1.097 \times 10^7 m__. **Step-by-Step Explanation:**
R=me48ϵ02h3cR = \frac{me^4}{8\epsilon_0^2 h^3 c}
Substituting: m = 9.1 _ 10___ kg, e = 1.6 _ 10___ C, __ = 8.85 _ 10___ C_/N�m_, h = 6.63 _ 10___ J�s, c = 3 _ 10_ m/s.
R=9.1×10−31×(1.6×10−19)48×(8.85×10−12)2×(6.63×10−34)3×3×108=1.097×107 m−1R = \frac{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} = 1.097 \times 10^7 \text{ m}^{-1}
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