Download App

ATOMS — Physics STD 12 Science — Question

Bihar BoardEnglish MediumSTD 12 SciencePhysicsATOMS2 Marks
Question
Using the formula for the radius of $n ^{\text {th }}$ orbit $r_n=\frac{n^2 h^2 \varepsilon_0}{\pi m e^2}$ derive an expression for the total energy of electron in $n^{\text {th }}$ Bohr's orbit.
✓

Answer

→From Bohr's second postulate, the formula for the radius of $n^{\text {th }}$ orbit for hydrogen atom is.
$r_n=\frac{n^2 h^2 \varepsilon_0}{\pi m e^2}$
→The total energy of the electron in the stationary states of the hydrogen atom is
$E _n=-\frac{1}{8 \pi \varepsilon_0} \frac{e^2}{r_n}$
→Using equation (1) and equation (2)
$E _n=-\frac{1}{8 \pi \varepsilon_0} \frac{e^2}{\left(\frac{ n ^2 h^2 \kappa_0}{\pi m e^2}\right)}$
$\therefore E _n=-\frac{m e^4}{8 \varepsilon_0{ }^2 n^2 h^2}$
→Substituting $m=9.1 \times 10^{-31} kg$
$\begin{array}{l}
e=1.6 \times 10^{-19} C \\
\varepsilon_0=8.85 \times 10^{-12} \frac{ C ^2}{ Nm ^2} \\
h=6.625 \times 10^{-34} Js
\end{array}$
→Simplifying equation,
$E _n=-\frac{2.18 \times 10^{-18}}{n^2} J$
→Atomic energies are often expressed in electron volts $(e V)$.
$\begin{array}{l} 
\therefore E _n=-\frac{2.18 \times 10^{-18}}{n^2 \times 1.6 \times 10^{-19}} eV \\
\therefore E _n=-\frac{13.6}{n^2} eV
\end{array}$
→The negative sign of the total energy of an electron moving in an orbit means that the electron is bound with the nucleus.
→Thus, energy will be required to remove the electron from the hydrogen atom to a distance infinitely far away from its nucleus.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Short Answer Type Questions [2M]" from ATOMS→ATOMS — all question types→Physics STD 12 Science question papers→Bihar Board STD 12 Science question papers→Bihar Board question paper generator→

Similar questions

The value of the Brewster angle for a transparent medium is different for lights of different colours.
→
  1. State the condition under which a large magnification can be achieved in an astronomical telescope.
  2. Give two reasons to explain why a reflecting telescope is preferred over a refracting telescope.
→
What is the longest wavelength of photon that can ionize a hydrogen atom in its ground state? Specify the type of radiation.
→
Define resolving power of a compound microscope. How does the resolving power of a compound microscope change when.
  1. refractive index of the medium between the object and objective lens increases?
  2. wavelength of the radiation used is increased?
→
If $\overrightarrow{\text{A}}\times\overrightarrow{\text{B}}=0,$ can you say that:

  1. $\overrightarrow{\text{A}}=\overrightarrow{\text{B}}$

  2. $\overrightarrow{\text{A}}\neq\overrightarrow{\text{B}}$

→
Write (or mention) the achievements of Maxwell's Electro Magnetic wave theory and Hertz's experiment.
→
Write down the conditions for constructive and destructive interference in terms of path difference.
→
What is quantization of charge?
→
What is the importance of radial magnetic field in a moving coil galvanometer ?
→
Draw 3 equipotential surfaces corresponding to a field that uniformly increases in magnitude but remains constant along Z-direction. How are these surfaces different from that of a constant electric field along Z-direction?
→