Electromagnetic radiation having time varying electric field $E = E_{0} (1 + \cos ω t) \cos ω_{0} t$ falls on a metal surface of work function $ϕ$ . If $ω > ω_{0}$ , the possible speed(s) of photoelectron is ( $ℏ (ω - ω_{0}) > ϕ > ℏ ω_{0}$ where $(ℏ = \frac{h}{2 π})$ )

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$\sqrt{\frac{2 (ℏ ω - ϕ)}{m}}$

$\sqrt{\frac{2}{m} \{ℏ (ω + ω_{0}) - ϕ\}}$

$\sqrt{\frac{2}{m} (ℏ ω_{0} - ϕ)}$

$\sqrt{\frac{2}{m} \{ℏ (ω - ω_{0}) - ϕ\}}$

answer is A, B, D.

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Detailed Solution

$\begin{array}{l} E = E_{0} (1 + \cos ω t) \cos ω_{0} t \\ = E_{0} \cos ω_{0} t + \frac{E_{0}}{2} \cos \{(ω + ω_{0}) t\} + \frac{E_{0}}{2} \cos \{(ω - ω_{0}) t\} \\ ∴ K_{max} = ħ (ω + ω_{0}) - ϕ \\ \Rightarrow V_{max} = \sqrt{\frac{2}{m} \{ħ (ω + ω_{0}) - ϕ\}} \end{array}$

As per question,

$\begin{array}{l} ℏ (ω - ω_{0}) > ϕ \\ \Rightarrow ℏ ω - ϕ > ℏ ω_{0} \\ S i n c e, ω_{0} i s p o s i t i v e \\ \Rightarrow (ℏ ω - ϕ) i s a l s o p o s i t i v e . \end{array}$