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GUJCET · Physics · Atoms
The radius of the inner most electron orbit of a hydrogen atom is \(5.3 \times 10^{-11} \mathrm{~m}\) ．What is the radius of the \(n=4\) state ？
- A \(8.48 \times 10^{-10} \mathrm{~m}\)
- B \(4.24 \times 10^{-10} \mathrm{~m}\)
- C \(2.12 \times 10^{-10} \mathrm{~m}\)
- D \(10.6 \times 10^{-10} \mathrm{~m}\)
Answer & Solution
Correct Answer
(A) \(8.48 \times 10^{-10} \mathrm{~m}\)
Step-by-step Solution
Detailed explanation
(A) \(8.48 \times 10^{-10} \mathrm{~m}\)
\(r_{n}=\frac{n^{2}}{Z} a_{0}\)
\(r_{4}=\frac{(4)^{2}}{(1)} \times 5.3 \times 10^{-11}\)
\(r_{4}=16 \times 5.3 \times 10^{-11}\)
\(r_{4} \approx 8.48 \times 10^{-10} \mathrm{~m}\)
\(r_{n}=\frac{n^{2}}{Z} a_{0}\)
\(r_{4}=\frac{(4)^{2}}{(1)} \times 5.3 \times 10^{-11}\)
\(r_{4}=16 \times 5.3 \times 10^{-11}\)
\(r_{4} \approx 8.48 \times 10^{-10} \mathrm{~m}\)
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