Question

The energy required to excite an electron from the first Bohr orbit of a hydrogen atom to the second Bohr orbit is:

• A. \(1.634\times 10^{-18}\,\text{J}\)
• B. \(1.2\times 10^{-19}\,\text{J}\)
• C. \(0.2\times 10^{-18}\,\text{J}\)
• D. \(1.2\times 10^{-20}\,\text{J}\)

Hint:

For hydrogen atom problems:
Use \(E_n=-\dfrac{13.6}{n^2}\,\text{eV}\)
Excitation energy is always positive (energy absorbed)
Ionization energy corresponds to transition from \(n=1\) to \(n=\infty\)

Answer 1

The Correct Option is A

Concept:
According to the Bohr model of the hydrogen atom, the energy of an electron in the \(n^\text{th}\) orbit is given by: \[ E_n = -\frac{13.6}{n^2}\ \text{eV} \] The energy required for excitation from one orbit to another is the difference in energies of the two orbits.
Step 1: Write energies of the first and second Bohr orbits. For the first orbit (\(n=1\)): \[ E_1 = -13.6\ \text{eV} \] For the second orbit (\(n=2\)): \[ E_2 = -\frac{13.6}{4} = -3.4\ \text{eV} \]
Step 2: Calculate the energy required for excitation. \[ \Delta E = E_2 - E_1 = (-3.4) - (-13.6) = 10.2\ \text{eV} \]
Step 3: Convert electron volts to joules. Using: \[ 1\ \text{eV} = 1.602\times 10^{-19}\ \text{J} \] \[ \Delta E = 10.2 \times 1.602\times 10^{-19} = 1.634\times 10^{-18}\ \text{J} \] \[ \boxed{\Delta E = 1.634\times 10^{-18}\ \text{J}} \]