Following results are observed when sodium metal is irradiated with different wavelengths. Calculate (a) threshold wavelength and (b) Planck's constant.
`{:(lambda(nm),,500 ,450,400),(vxx10^(-5)(cm s^(-1)),,2.55,4.35,5.35):}`

Explanation

Suppose threshold wavelength `=lambda_(0) nm=lambda_(0)xx10^(-9) m`
Then `h(v-v_(0))=1/2 mv^(2)` or `hc(1/lambda-1/lambda_(0))=1/2 mv^(2)`
Substituting the given results of the three experiments, we get
`(hc)/10^(-9)(1/500-1/lambda_(0))=1/2 m(2.55xx10^(6))^(2) ...(i)`
`(hc)/10^(-9)(1/450-1/lambda_(0))=1/2m(4.35xx10^(6))^(2) ...(ii)`
`(hc)/10^(-9)(1/400-1/lambda_(0))=1/2m(5.20xx10^(6))^(2) ...(iii)`
Dividing equation (ii) by equation (i), we get
`(lambda_(0)-450)/(450lambda_(0))xx(500lambda_(0))/(lambda-500)=(4.35/2.55)^(2)`
or `(lambda_(0)-450)/(lambda_(0)-500)=450/500xx(4.35/2.55)^(2)=2.619`
or `lambda_(0)-450=2.619 lambda-1309.5`
or `1.619 lambda_(0)=859.5 rArr lambda_(0)=531 nm`
Subtituting this value of equation (iii), we get
`(hxx(3xx10^(8)))/10^(-9)(1/400-1/531)=1/2(9.11xx10^(-31))xx(5.20xx10^(6))^(2)`
`h=6.66xx10^(-34)J s`