A freshly prepared sample of $H_{2}$ gas having all tritium atoms $(^{3} H)$ with half-life 12.3 years occupies 125 mL at 500 kPa and 300 K. The activity of the sample is:

1448 C i

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3548 C i

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2645 C i

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none of these

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Solution

The correct option is A $1448 C i$
$n = \frac{P V}{R T} = \frac{500 k P a \times \frac{1 a t m}{101.325 k P a} \times 0.125 L}{1 \times 0.0821 L a t m / m o l / K \times 300 K} = 0.025 m o l$

$λ = \frac{0.693}{t_{1 / 2}} = \frac{0.693}{12.3 \times 365 \times 24 \times 3600}$

$\frac{- d N}{d t} = λ N = \frac{0.693}{12.3 \times 365 \times 24 \times 3600} \times 0.025 \times 2 \times 6.023 \times 10^{23} \times \frac{1 C i}{3.7 \times 10^{10} d p s} \approx 1448 C i$

Thus, the activity of the sample is $1448 C i$

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Similar questions

125 {cm}^{3}

(^{3} H, t_{\frac{1}{2}} = 12.3 years)

500 k Pa

300 K .

[Take Bolzmann constant k_{B} = 1.38 \times 10^{- 23} {JK}^{- 1}]

A vessel of volume 125 $c m^{3}$ contains tritium $(^{3} H, t_{\frac{1}{2}}$ = 12.3 y) at 500 kPa and 300 K. Calculate the activity of the gas.

4 \times 10^{23}

2.3 years

_{1}^{3} H

_{1}^{1} H

8.0 \times 10^{- 18} : 1

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