A gas of hydrogen-like ions is prepared in a particular excited. State A. It emits photons having wavelength equal to the wavelength of the first line of the Lyman series together with photons of five other wavelengths. Identify the gas and find the principal quantum number of the state A.

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Solution

Formula,

$\frac{n (n - 1)}{2}$

total of 6 photons,

$\frac{n (n - 1)}{2} = 6$

$∴ n = 4$

therefore, the principal quantum number is $4$ and the gas is in $4 t h$ excited state

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A gas of hydrogen-like ions is prepared in a particular excited. State A. It emits photons having wavelength equal to the wavelength of the first line of the Lyman series together with photons of five other wavelengths. Identify the gas and find the principal quantum number of the state A.

Formula,n(n−1)2total of 6 photons,n(n−1)2=6∴n=4therefore, the principal quantum number is 4 and the gas is in 4th excited state

Formula,

$\frac{n (n - 1)}{2}$

total of 6 photons,

$\frac{n (n - 1)}{2} = 6$

$∴ n = 4$

therefore, the principal quantum number is $4$ and the gas is in $4 t h$ excited state