Bohr's Model Of An Atom - Practice Questions & MCQ

Bohr's model and its postulates:

1. The electron in the hydrogen atom can move around the nucleus in a circular path of fixed radius and energy. These paths are called orbits, stationary states or allowed energy states and are arranged concentrically around the nucleus. Force of attraction between the nucleus and an electron provides the centripetal force required by the electron to carry out the circular motion.

2. The energy of an electron in the orbit does not change with time. However, the electron will move from a lower stationary state to a higher stationary state when required amount of energy is absorbed by the electron or energy is emitted when electron moves from higher stationary state to lower stationary state

3. Energy can be absorbed or emitted when electron transitions between two different orbits and the frequency of photon involved can be calculated using the formula:

                         $\left|E_1-E_2\right|=h \nu$

4. The angular momentum of an electron is quantised. In a given stationary state it can be expressed as

           L= mvr= nh/2$\pi$, n = orbit number

So only those energy states (or orbits) are allowed in which the above equation holds true for the angular momentum.

Note: Bohr's model is only valid for Hydrogen like species or unielectronic species which contain only a single electron

According to Bohr’s theory for hydrogen atom: 

(1) The stationary states for electron are numbered n = 1,2,3.......... These integral numbers are known as Principal quantum numbers.

(2) Bohr radius of nth orbit:

$\mathrm{r}_{\mathrm{n}}=0.529 \frac{\mathrm{n}^2}{\mathrm{Z}} \mathrm{A}^0$

where Z is atomic number and radius is calculated by the formula in angstrom (A⁰)  (1A⁰=10^-10 m)

(3) Velocity of electron in nth orbit:

$\mathrm{V}_{\mathrm{n}}=\left(2.18 \times 10^6\right) \frac{\mathrm{Z}}{\mathrm{n}} \mathrm{m} / \mathrm{s}$

where Z is atomic number

(4) Total energy of electron in nth orbit:

$E_n=-13.6 \frac{Z^2}{n^2} \mathrm{eV}=-2.18 \times 10^{-18} \frac{Z^2}{n^2} \mathrm{~J}$

where Z is atomic number

Depending upon the units given in the question, the respective formula can be used

(5) Time Period and Frequency of Revolution

        Although the precise equations for time period and frequency of revolution are not required but still it is a good idea to look at the variations of these with the atomic number (Z) and the orbit number (n).

We know that Time period (T) is the time required for one complete revolution and that Frequency ($\nu$) is inverse of the time period

$\therefore T=\frac{\text { distance }}{\text { time }}=\frac{2 \pi r}{v}$

$\because r \propto \frac{\mathrm{n}^2}{\mathrm{Z}}$ and $v \propto \frac{\mathrm{Z}}{\mathrm{n}}$

$\therefore T \propto\left(\frac{n^2}{Z} \times \frac{n}{Z}\right) \propto\left(\frac{n^3}{Z^2}\right)$

$\therefore \nu=\left(\frac{1}{T}\right) \propto\left(\frac{Z^2}{n^3}\right)$

It is important that you remember all the above formula and relations