If the speed of an electron of hydrogen atom in the ground state is 2.2×106ms , then its speed in the third excited state will be

MHT CET · Physics · Atomic Physics

If the speed of an electron of hydrogen atom in the ground state is $2.2 \times \frac{10^{6} m}{s}$ , then its speed in the third excited state will be

A $5.5 \times \frac{10^{6} m}{s}$
B $5.5 \times \frac{10^{5} m}{s}$
C $8.8 \times \frac{10^{5} m}{s}$
D $6.8 \times \frac{10^{6} m}{s}$

Verified Solution

Answer & Solution

Correct Answer

(B) $5.5 \times \frac{10^{5} m}{s}$

Step-by-step Solution

Detailed explanation

Speed of electron of hydrogen atom in ground state,

v_{1} = 22 \times \frac{10^{6} m}{s}

Since,

v \propto \frac{1}{n}

∴ \frac{v_{1}}{v_{2}} = \frac{n_{2}}{n_{1}} = \frac{2.2 \times 10^{6}}{v_{2}}

[for third excited state,

n_{2} = 4

]

\Rightarrow v_{2} = \frac{2.2 \times 10^{6}}{4} = 0.55 \times \frac{10^{6} m}{s}

= 5.5 \times \frac{10^{5} m}{s}

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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