1. Tardigrade
  2. Question
  3. Chemistry
  4. Energy of an electron is given by E=-2.178 × 10-18 J ((Z2/n2)).Wavelength of light required to excite an electron in an hydrogen atom from level n=1 to n=2 will be (h= 6.62 × 10-34 Js text and c=3.0 × 108 ms -1)

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Q. Energy of an electron is given by $E=-2.178 \times 10^{-18} J$ $\left(\frac{Z^{2}}{n^{2}}\right)$.Wavelength of light required to excite an electron in an hydrogen atom from level $n=1$ to $n=2$ will be
$\left(h= 6.62 \times 10^{-34} Js\text { and } c=3.0 \times 10^{8} ms ^{-1}\right)$

JEE MainJEE Main 2013Structure of Atom

Solution:

Given, in the question $E=-2.178 \times 10^{-18} J \left[\frac{Z^{2}}{n^{2}}\right]$
For hydrogen $ Z=1$,
So, $E_{1}=-2.178 \times 10^{-18} J \left[\frac{1}{1^{2}}\right]$
$E_{2}=-2.178 \times 10^{-18} J \left[\frac{1}{2^{2}}\right]$
Now, $E_{1}-E_{2}$
i.e. $\Delta E=2.178 \times 10^{-18}\left(\frac{1}{1^{2}}-\frac{1}{2^{2}}\right)=\frac{h c}{\lambda}$
$2.178 \times 10^{-18}\left(\frac{1}{1^{2}}-\frac{1}{2^{2}}\right)=\frac{6.62 \times 10^{-34} \times 3.0 \times 10^{8}}{\lambda}$
$\therefore \lambda \approx 1.21 \times 10^{-7} m$