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QPages 352-354: Q8: HC Verma: Concepts of Physics - Volume 2 Electric Current through Gases Pages 352-354: Q8 Solution: If the temperature of a tungsten filament is raised from 2000 K …

⚠️ Common Exam Traps & Conceptual Pitfalls

When calculating the ratio of emission currents, students frequently drop the negative sign in the exponent term $e^{-\frac{\phi}{k}(\frac{1}{T_2} - \frac{1}{T_1})}$, leading to an incorrect decrease in current. Always verify that the exponent is positive when $T_2 > T_1$ because the term $(\frac{1}{T_2} - \frac{1}{T_1})$ is negative, which cancels the leading negative sign.

If the temperature of a tungsten filament is raised from 2000 K to 2010 K, by what factor does the emission current change? Work function of tungsten is 4.5 eV.

Step-by-Step Verified Solution

**Answer:** The emission current changes by a factor of 1.14. **Step-by-Step Explanation:** i∝T2e−ϕ/kTi \propto T^2 e^{-\phi/kT}.
i′i=(20102000)2e−ϕk(12010−12000)\frac{i'}{i} = \left(\frac{2010}{2000}\right)^2 e^{-\frac{\phi}{k}\left(\frac{1}{2010} - \frac{1}{2000}\right)}
=(1.005)2e−4.5×1.6×10−191.38×10−23×(−102000×2010)= (1.005)^2 e^{-\frac{4.5 \times 1.6 \times 10^{-19}}{1.38 \times 10^{-23}} \times \left(\frac{-10}{2000 \times 2010}\right)}
=1.01×e0.13=1.01×1.139=1.15≈1.14= 1.01 \times e^{0.13} = 1.01 \times 1.139 = 1.15 \approx 1.14

All Questions in this Chapter

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