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Question: An electron tube was sealed off during manufacture at a pressure of \(1.2 \times 10^{- 7}\)mm of mer...

An electron tube was sealed off during manufacture at a pressure of 1.2×10−71.2 \times 10^{- 7}mm of mercury at 27°C. Its volume is 100 cm3. The number of molecules that remain in the tube is

A

2×10162 \times 10^{16}

B

3×10153 \times 10^{15}

C

3.86×10113.86 \times 10^{11}

D

5×10115 \times 10^{11}

Answer

3.86×10113.86 \times 10^{11}

Explanation

Solution

Gas equation for N molecules PV=NkTPV = NkT

ŽN=PVkT=1.2×10−10×13.6×103×10×10−41.38×10−23×300N = \frac{PV}{kT} = \frac{1.2 \times 10^{- 10} \times 13.6 \times 10^{3} \times 10 \times 10^{- 4}}{1.38 \times 10^{- 23} \times 300}

=3.86×1011= 3.86 \times 10^{11}