Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 12
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# A Tungsten Cathode and a Thoriated-tungsten Cathode Have the Same Geometric Dimensions and Are Operated at the Same Temperature. - Physics

ConceptDavisson-Germer Experiment

#### Question

A tungsten cathode and a thoriated-tungsten cathode have the same geometric dimensions and are operated at the same temperature. The thoriated-tungsten cathode gives 5000 times more current than the other cathode. The constant A in the Richardson−Dushman equation is 60 × 104 Am −2 K−2 for pure tungsten and 3.0 × 104 Am −2 k−2 for thoriated tungsten. The work function of pure tungsten is 4.5 eV and that of thoriated tungsten is 2.6 eV. Find the operating temperature.

#### Solution

For the pure tungsten cathode,

work function, ϕ = 4.5 eV

A = 60 × 104 Am −2 K−2

For the thoriated-tungsten cathode

work function, ϕ = 2.6 eV

A = 3.0 × 104 Am−2K−2

Saturation current,

$i = AS T^2 e^{- \phi/KT}$

For thoriated tungsten,

$i_{\text{Thorited Tungsten}} = 5000 i_{\text{Tungsten}}$

So,

$\Rightarrow S \times 3 \times {10}^4 \times T^2 \times e^\frac{- 2 . 6 \times 1 . 6 \times {10}^{- 19}}{1 . 38 \times {10}^{- 23} \times T} = 5000 \times 60 \times {10}^4 \times S \times T^2 \times e^\frac{- 4 . 5 \times 1 . 6 \times {10}^{- 19}}{1 . 38 \times T \times {10}^{- 23}}$

$\Rightarrow e^\frac{- 2 . 5 \times 1 . 6 \times {10}^{- 19}}{1 . 38 \times {10}^{- 23} \times T} = {10}^5 \times e^\frac{- 4 . 5 \times 1 . 6 \times {10}^{- 19}}{1 . 38 \times {10}^{- 23} \times T}$

Taking 'ln' of both sides, we get:-

$\frac{- 2 . 89 \times {10}^4}{T} = 11 . 51 + \frac{- 5 . 22 \times {10}^4}{T}$

$\Rightarrow 11 . 51T = 2 . 33 \times {10}^4$

$\Rightarrow T = 2024 K$

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Solution A Tungsten Cathode and a Thoriated-tungsten Cathode Have the Same Geometric Dimensions and Are Operated at the Same Temperature. Concept: Davisson-Germer Experiment.
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