KVPY SX SB Exam 05-Nov-2017 Question Paper

Question : 40 of 120

Marks: +1, -0

The number of gas molecules striking per second per square meter of the top surface of a table placed in a room at 20°C and 1 atmospheric pressure is of the order of

(k_B = 1.4 × 10^{–23}

J/K, and the average mass of an air molecules is 5 × 10

^{–27}

kg)

10 $^{27}$
10 $^{23}$
10 $^{25 }$
10 $^{29}$

Validate

Solution:

V_\rms=√{{3RT}/M}=√{{3kT}/0}

P = N × 2mV_\rms

1.01 × 10^5 = N × 2 × 5 × 10^{–27} × V_\rms

N={{1.01 × 10^5 √{ 5 × 10^{–27}}}/{2× 5 × 10^{–27}√{3 ×1.4×10^{23}×293}

= 6.43×10^27

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