Question

In a Bohr's model of an atom, when an electron jumps from n = 1 to n = 3, how much energy will be absorbed?

• A. $2.389\times 10^{-12}$ ergs
• B. $0.239\times 10^{-10}$ ergs
• C. $2.15\times 10^{-11}$ ergs
• D. $0.1936\times 10^{-10}$ ergs

Answer 1

Answer: (D)

Energy of an atom when $n=1$
$E_1=-\frac{1312}{(1{)}^2}=-1312kJmo{l}^{-1}$
Similarly energy when $n=3,\left(E_3\right)=-\frac{1312}{(3{)}^2}$
$=-145.7kJmo{l}^{-1}$
The energy absorbed when an electron jumps from $n=1$ to $n=3$
$E_3-E_1=-145.7-\left(-1312\right)=1166.3\text{ kJ mo}{\left(\text{l}\right)}^{-1}$
$=\frac{1166.3}{6.023\times 10^{23}}=193.6\times 10^{-23}kJ$
$=193.6\times 10^{-20}J\left[\text{1 Joule}=10^7\text{ ergs}\right]$
$193.6\times 10^{-13}ergs=0.1936\times 10^{-10}ergs$