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A metal is illumimated by light of two d...

A metal is illumimated by light of two different wavelength `248nm` and `310 nm` . The maximum speeds of the photoelecrtron corresponding in these wavwlength are ``u_(1) and u_(2)` respectively . If the ratio u_(1) : u_(2) = 2 : 1 ` and `hc = 1240 eVnm `, the work function of the inetial is rearly

A

`3.7 eV`

B

`3.2 eV`

C

`2.8eV`

D

`2.5 eV`

Text Solution

Verified by Experts

The correct Answer is:
A
`(hC)/(lambda_(1)) W = (1)/(2) mu_(1)^(2)`
`and ((hC)/(lambda_(2)) W = (1)/(2) mu_(2)^(2)``
Dividing the above two equation , we get
` ((hC)/(lambda_(1)) - W)/((hC)/(lambda_(2)) - W) ((hC)/(lambda_(1)) - W)/((hC)/(lambda_(2)) - W) (u_(1)^(2)/(u_(2)^(2)`
` :. `((1240)/(248) -W)/((1240)/(310) -W = (4)/(1)`
`:. (1240)/(248) -W = (4 xx 1240)/(310) - 4W`
`:. W = 3.7 eV`
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