Electro magnetic waves of wavelength $1242 A^{0}$ are incident on a metal of work function 2eV. The target metal is connected to a 5V cell as shown. The electron pass through a hole A into a gas of hydrogen atoms in their ground state. Find the number of spectral lines emitted when hydrogen atoms come back to their ground state after having been excited by the electrons. Assume all excitations in H atoms from ground state only $(h c = 12420 e V A^{0})$

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answer is 6.

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Detailed Solution

$K E_{\max} = \frac{h c}{λ} - ω_{0} = 8 e V$

$Δ K E = 0 t o 8 e V$

$K E^{1} = 5 e V t o 13 e V$

So n = 4

$N = \frac{n (n - 1)}{2} = \frac{4 \times 3}{2} = 6$

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