A long solenoid of 20 turns/ cm carries a current of 1.0 A. Radiation of wavelength `lamda` fall on a target placed within the solenoid. It is observed that electrons emitted move in a circle of largest radius 1 cm. Find the value of `lamda`. Given work function is 1 eV:

Options

A. `1000Å`
B. `7975Å`
C. `5000Å`
D. `8320Å`

Answer

B

Explanation

Magnetic field within solenoid is
`B= mu_(0)ni`
`=4pi xx10^(-7)xx20xx100xx1*0=8pixx10^(-4)T`
The speed v of the ejected electron is given by
`(mv^(2))/(r)=evB or v=(eBr)/(m)`
Then `v=4*46xx10^(6)m//s`
Now `(hc)/(lambda)=w+(1)/(2)mv^(2)`
`=1eV+(1)/(2)xx9xx10^(-31)(4*46xx10^(6))^(2)`
`=1*6xx10^(-19)+0*89xx10^(-19)`
`rArr E=2*49xx0^(-19)` Now `lambda=(hc)/(E)`
`:. lambda=(hc)/(2*49xx10^(-19))`
`=(6*62xx10^(-34)xx3xx10^(8))/(2*49xx10^(-19))`
or `lambda=7*675xx10^(-7)m=79757Å`