Question

An excited hydrogen atom emits light with a wavelength of 397.2
nm to reach the

energy level for which n = 2. In which principal quantum level did
the electron

begin? (c = 3.00 x 108 m/s, h = 6.63 x 10-34 J•s, RH = 2.18 x
10-18J).

Answer #1

According to Rydberg equation

= R_{H} × ( _{
} - _{
)}

given,
= 397.2 nm = 397.2 ×10^{-9} m .

n_{i} = 2

R_{H} = 2.18×10^{-18} J = (
2.18×10^{-18} ×
) m^{-1}

= 2.18×10^{-18} × _{
} m^{-1}

= 1.096 ×10^{7} m^{-1} .

so,

= 1.096 × 10^{7} (
- _{
} )

or, (
- _{
} ) = _{
}

or, _{
} = (
- 0.2296 )

or, _{
} = 0.0205

or, n_{f}^{2} = 49

or, n_{f} = 7.

Hence, the electron began at principal quantum number 7.

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