The Rutherford - Royds experiment. The following experiment dates from 1909. The apparatus is shown below. The thin - walled glass flask, containing radon (an a emitter), is placed inside the thick-walled glass apparatus. The apparatus is evacuated, and the valve to the vacuum pump is then closed. After a week, additional mercury is added to the apparatus until the liquid level reaches the bottom of the tube. A high-voltage discharge is then passed through the tube, and the light emitted is observed with a spectrometer. The flask emits a-particles when Radon decays according to equation with a half life of 3.5 days. The flask contained 222 gm of radioactive Radon. We can assume that half of the a-particles emitted accumulate in the empty space above mercury. The volume of tube is 1 litre. Take density of mercury as 13.6 gm/cc. Assume that a-particles can combine with 1 free electron or 2 free electrons to form Helium gas, or singly ionized Helium in ground state.(Take : Atmospheric pressure 105 Pa, temperature = 27°C, R = 25/3 J/mol-K)

The Rutherford - Royds experiment. The following experiment dates from 1909. The apparatus is shown below. The thin - walled glass flask, containing radon (an a emitter), is placed inside the thick-walled glass apparatus. The apparatus is evacuated, and the valve to the vacuum pump is then closed. After a week, additional mercury is added to the apparatus until the liquid level reaches the bottom of the tube. A high-voltage discharge is then passed through the tube, and the light emitted is observed with a spectrometer. The flask emits a-particles when Radon decays according to equation

$_{86}^{222} Rn \overset{}{\to}_{84}^{218} Po +_{2}^{4} He$

with a half life of 3.5 days. The flask contained 222 gm of radioactive Radon. We can assume that half of the a-particles emitted accumulate in the empty space above mercury. The volume of tube is 1 litre. Take density of mercury as 13.6 gm/cc. Assume that a-particles can combine with 1 free electron or 2 free electrons to form Helium gas, or singly ionized Helium in ground state.

(Take : Atmospheric pressure 10⁵ Pa, temperature = 27°C, R = 25/3 J/mol-K)

Linked Question 1

What is the pressure at point A.

9.375 atm.

18.75 atm.

0.32 atm

3.25 atm.

PV = nRT ⇒ P × 10^–3 = $\frac{3}{8} \times \frac{25}{3} \times 300$ ⇒ P = 9.375

Linked Question 2

How many moles of Helium gas is present in the capillarly tube.

0.5 mole

0.75 mole

0.68 moles

0.375 ,ole

$N_{t} = \frac{N_{0}}{2^{\frac{t}{t_{1 / 2}}}} = \frac{N_{0}}{2^{7 / 3 .5}} = \frac{N_{0}}{4} \frac{3 N_{0}}{4}$

$∴$ Number of nuclei decayed =

Given that half of α-particle emitted accumulate in the empty space above mercury.

So no. of moles of He gas

$= \frac{3 N_{0}}{8 N_{0}} = 0 .375 moles$

Linked Question 3

What should be the minimum voltage of the discharge to obtain spectra emitted by singly ionized Helium gas ?

13.6 V

54.4 V

10.2 V

40.8 V

$13 .6 \times 2^{2} (1 - \frac{1}{2^{2}})$