Ncert Exercises & Solutions

2.19 The electron energy in hydrogen atom is given by En = (–2.18 × 10–18 )/n2 J. Calculate the energy required to remove an electron completely from the n = 2 orbit. What is the longest wavelength of light in cm that can be used to cause this transition?

Given,

E_{n} = - \frac{2.18 x 10^{- 19}}{n^{2}} J

Energy required for ionization from n = 2 is given by,

∆ E = E_{\infty} - E_{2}

= [(\frac{- 2.18 x 10^{- 18}}{{(\infty)}^{2}}) - (\frac{- 2.18 x 10^{- 18}}{{(2)}^{2}})] J

= [\frac{2.18 x 10^{- 18}}{4} - 0] J

= 0.545 \times 10^{- 18} J

∆ E = 5.45 \times 10 - 19 J

λ = \frac{hc}{∆ E}

Here, λ is the longest wavelength causing the transition .

λ = \frac{(6.626 x 10^{- 34}) (3 x 10^{8})}{5.45 x 10^{- 19}} = 3.647 x 10^{- 7} m

= 3647 \times 10 - 10 m

= 3647 Å

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