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Junior Executive (AO) Official Paper 1: Held on Sep 2016

Option 4 : 0.477 nm

General Principles of Business Management - 1

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__Bohr's Atomic Model__:

Bohr proposed a model for hydrogen atom which is also applicable for some lighter atoms in which a single electron revolves around a stationary nucleus of positive charge Ze (called hydrogen-like atom).

Bohr's model is based on the following postulates:

He postulated that an electron in an atom can move around the nucleus in certain circular stable orbits without emitting radiations.

Bohr found that the magnitude of the electron's angular momentum is quantized i.e.

\(L = m{v_n}\;{r_n} = n\left( {\frac{h}{{2\pi }}} \right)\)

Where n = 1, 2, 3, ..... each value of n corresponds to a permitted value of the orbit radius, rn = Radius of nth orbit, vn = corresponding speed and h = = Planck's constant

The radiation of energy occurs only when an electron jumps from one permitted orbit to another.

According to the Bohr model of the hydrogen atom, the radius of the nth orbit is given as,

\( {r_n} = {n^2}{r_1}....(1)\)

where n = number of orbit and r1 = radius of the first orbit

__Calculation__:

Given that, n_{1} = 1, r_{1} = 0.053 nm , n_{3} = 3 , Z = 1( mass number of hydrogen)

The radius of the n^{th} orbit is,

\( {r_n} = {n^2}{r_1}....(1)\)

\({r_n} = {3^2} \times 0.053 = 0.477 \;nm\)

**The radius of n ^{th} orbit is 0.477 nm **