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Standard XII

Physics

Characteristics of Bohr's Atomic Model

The electron ...

Question

The electron in a hydrogen atom makes a transition from $n_{1}$ to $n_{2}$ state. The time period of the electron in $n_{1}$ is 8 times of that in $n_{2}$ .The possible values of $n_{1}$ and $n_{2}$ are:

n_{1} = 8, n_{2} = 1

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n_{1} = 4, n_{2} = 2

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n_{1} = 2, n_{2} = 4

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n_{1} = 1, n_{2} = 8

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Solution

The correct option is D $n_{1} = 4, n_{2} = 2$
Time period $T \propto n^{3}$
Given : $T_{1} = 8 T_{2}$
$∴$ $\frac{T_{1}}{T_{2}} = (\frac{n_{1}}{n_{2}})^{3}$

OR $8 = (\frac{n_{1}}{n_{2}})^{3}$ $⟹ n_{1} = 2 n_{2}$
$⟹$ $n_{2} = 2$ and $n_{1} = 4$ is the possible answer.

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The electron in a hydrogen atom makes a transition from n1 to n2 state. The time period of the electron in n1 is 8 times of that in n2.The possible values of n1 and n2 are:

The correct option is D n1=4,n2=2Time period T∝n3Given : T1=8T2∴ T1T2=(n1n2)3OR 8=(n1n2)3 ⟹n1=2n2⟹ n2=2 and n1=4 is the possible answer.

The electron in a hydrogen atom makes a transition from $n_{1}$ to $n_{2}$ state. The time period of the electron in $n_{1}$ is 8 times of that in $n_{2}$ .The possible values of $n_{1}$ and $n_{2}$ are:

The correct option is D $n_{1} = 4, n_{2} = 2$
Time period $T \propto n^{3}$
Given : $T_{1} = 8 T_{2}$
$∴$ $\frac{T_{1}}{T_{2}} = (\frac{n_{1}}{n_{2}})^{3}$

OR $8 = (\frac{n_{1}}{n_{2}})^{3}$ $⟹ n_{1} = 2 n_{2}$
$⟹$ $n_{2} = 2$ and $n_{1} = 4$ is the possible answer.