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Following results are observed when sodi...

Following results are observed when sodium metal is irradiated with different wavelengths. Calculate (a) threshold wavelength and (b) Planck's constant.
`{:(lambda(nm),,5000,450,400),(vxx10^(-5)(cm s^(-1)),,2.55,4.35,5.35):}`

Text Solution

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Suppose threshold wavelength `=lambda_(0)nm=lambda_(0)xx10^(-9)m`
Also, `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)" ...(A)"`
`(hc)/(10(-9))((1)/(450)-(1)/(lambda_(0)))=(1)/(2)m(4.35xx10^(6))^(2)" ...(B)"`
`(hc)/(10^(-9))((1)/(400)-(1)/(lambda_(0)))=(1)/(2)m(5.20xx10^(6))^(2)" ....(C)"`
Dividing eqn.(B) by eqn. (A), we get
`"Or "(lambda_(0)-450)/(lambda-500)xx(450)/(500)=((4.35)/(2.55))^(2)=2.910" or "lambda_(0)-450=2.619lambda_(0)-1309.5`
`"Or "1.619 lambda_(0)=8.596 therefore lambda_(0)=531nm" Substituting this value in eqn. (C), we get"`
`(hxx(3xx10^(8)))/(10^(-9))((1)/(400)-(1)/(531))=(1)/(2)(9.11xx10^(-31))(5.20xx10^(6))^(2)" or "h=6.66xx10^(-34)Js`
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