If the ionisation energy of a hydrogen like Bohr atom is 4 Rydberg, then the wavelengths of radiation emitted when the electron jumps from first excited state to the ground state and the radius of the first orbit of this atom are:

3.04 \circ A, 0.53 \circ A

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304 \circ A, 0.265 \circ A

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912 \circ A, 0.53 \circ A

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3.04 \circ A, 0.265 \circ A

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Solution

The correct option is B $304 \circ A, 0.265 \circ A$
$\begin{matrix} Ionisation energy, E = R z^{2} \begin{matrix} R z^{2} & = 4 R z & = 2 \end{matrix} \end{matrix}$

$Radius of 1st orbit is \frac{0.529}{2} A^{0} =0.265 A^{0}$

$\begin{matrix} wavelength \frac{1}{λ} = R z^{2} [\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}}] \end{matrix}$

$\begin{matrix} n_{1} = 1 & n_{2} = 2 we get, & λ = 304 A^{0} \end{matrix}$

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If the ionisation energy of a hydrogen like Bohr atom is 4 Rydberg, then the wavelengths of radiation emitted when the electron jumps from first excited state to the ground state and the radius of the first orbit of this atom are:

The correct option is B 304∘A,0.265∘A Ionisation energy, E=Rz2Rz2=4Rz=2 Radius of 1st orbit is 0.5292A0=0.265A0 wavelength 1λ=Rz2[1n21−1n22]n1=1n2=2 we get, λ=304A0