One implication of Bohr's proposal is that electrons can exist only in certain…

CHEMISTRY · Multi-part · CBSE · Chemistry · Structure of Atom · Structure of Atom

Problem

One implication of Bohr's proposal is that electrons can exist only in certain allowable orbits, orbits in which electrons would not radiate electromagnetic radiation. The radii of these orbits were given by the equation

r_n = n^2 r_1,

where

n

is an integer and

r_1

—called the Bohr radius—is the smallest radius of orbit in which an electron can exist. (1) a** Using Coulomb's law, show that the Bohr radius,

r_1

, can be

\text{expressed as } r_1 = k \frac{e^2}{mv^2},

where

k

is the Coulomb constant,

e

is the charge on the electron (and on the proton),

m

is the mass of the electron and

v

is the orbital speed of the electron. (2) b** Using Bohr's idea that the angular momentum of the electron must be quantised in units of

\frac{h}{2\pi}

, show that the Bohr radius can be expressed as

r_1 = \frac{h^2}{4\pi^2 k e^2 m},

where

k

is the Coulomb constant. (3) c** Using the following data to show that the Bohr radius is about

0.53 \times 10^{-10}

m. -

h = 6.63 \times 10^{-34}

J s -

k = 9 \times 10^9

Nm²C^-2 -

e = -1.6 \times 10^{-19}

C -

m = 9.1 \times 10^{-31}

kg (4) d** What will the radii of the orbits be for which

n = 2, 3

and

4

Related theory

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