Question 584: Atoms & Nuclei

Question

An electron of a stationary hydrogen atom passes from the fifth energy level to the ground level. The velocity that the atom acquired as a result of photon emission will be

Accepted Answer

We know,
$${1 \over \lambda } = R{Z^2}\left( {{1 \over {n_1^2}} - {1 \over {n_2^2}}} ight)$$
where R = Rydberg constant, Z = atomic number
Here, n
1
= 1, n
2
= 5
$$ 	herefore $$ $${1 \over \lambda } = R\left( {{1 \over {{1^2}}} - {1 \over {{5^2}}}} ight)$$ = $${{24R} \over {25}}$$
According to conservation of linear momentum, we
get
Momentum of photon = Momentum of atom
$$ \Rightarrow $$ $${h \over \lambda }$$ = mv
$$ \Rightarrow $$ v = $${h \over {m\lambda }}$$ = $${h \over m}\left( {{{24R} \over {25}}} ight)$$ = $${{24hR} \over {25m}}$$

Answer

$${{24hR} \over {25m}}$$

Answer

$${{25hR} \over {24m}}$$

Answer

$${{25m} \over {24hR}}$$

Answer

$${{24m} \over {25hR}}$$

Atoms & Nuclei

An electron of a stationary hydrogen atom passes from the fifth energy level to the ground level. The velocity that the atom acquired as a result of photon emission will be

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