For the same objective, find the ratio of the least separation between two points to be distinguished by a microscope for light of `5000Å` and electrons accelerated through 100 V used as the illuminating substance.
For the same objective, find the ratio of the least separation between two points to be distinguished by a microscope for light of `5000Å` and electrons accelerated through 100 V used as the illuminating substance.
Text Solution
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Formula of linear limit of resolution of compound microscope having oil immersion objective is :
`d_(m)=(1.22lamda)/(2nsinbeta)`
Now resolution power,
`P=(1)/(d_(m))=(2nsinbeta)/(1.22lamda)`
`:.Pprop(1)/(lamda)`
`:.(P_(1))/(p_(2))=(lamda_(2))/(lamda_(1))" "......(1)`
Here, in the second case
`W=DeltaK`
`:.Ve=(1)/(2)mv^(2)=(P^(2))/(2m)" "(":.P=mv)`
`:.Ve=(h^(2))/(2mlamda^(2))`
( `"":.P=(h)/(lamda)` h=Planck.s constant)
`:.lamda^(2)=(h^(2))/(2Vem)`
`:.lamda=(h)/(sqrt(2Vem))`
`:.lamda_(2)=(h)/(sqrt(2Vem))" "(":.` In the second case `lamda=lamda_(2)`)
`:.lamda_(2)=(6.625xx10^(-34))/(sqrt(2xx100xx1.6xx10^(-19)xx9.1xx10^(-31)))`
`:.lamda_(2)=(6.625xx10^(-9))/(sqrt(200xx1.6xx9.1))m`
`:.lamda_(2)=(6.625xx10^(-9))/(sqrt(200xx1.6xx9.1))xx10^(10)Å`
`=(66.25)/(sqrt(200xx1.6xx9.1))` `=(66.25)/(53.96)`
`:.lamda_(2)=1.2278Å`
Now from equation (1),
`(P_(1))/(P_(2))=(1.2278)/(5000)`
`:.(P_(1))/(P_(2))=2.456xx10^(-4)`
`d_(m)=(1.22lamda)/(2nsinbeta)`
Now resolution power,
`P=(1)/(d_(m))=(2nsinbeta)/(1.22lamda)`
`:.Pprop(1)/(lamda)`
`:.(P_(1))/(p_(2))=(lamda_(2))/(lamda_(1))" "......(1)`
Here, in the second case
`W=DeltaK`
`:.Ve=(1)/(2)mv^(2)=(P^(2))/(2m)" "(":.P=mv)`
`:.Ve=(h^(2))/(2mlamda^(2))`
( `"":.P=(h)/(lamda)` h=Planck.s constant)
`:.lamda^(2)=(h^(2))/(2Vem)`
`:.lamda=(h)/(sqrt(2Vem))`
`:.lamda_(2)=(h)/(sqrt(2Vem))" "(":.` In the second case `lamda=lamda_(2)`)
`:.lamda_(2)=(6.625xx10^(-34))/(sqrt(2xx100xx1.6xx10^(-19)xx9.1xx10^(-31)))`
`:.lamda_(2)=(6.625xx10^(-9))/(sqrt(200xx1.6xx9.1))m`
`:.lamda_(2)=(6.625xx10^(-9))/(sqrt(200xx1.6xx9.1))xx10^(10)Å`
`=(66.25)/(sqrt(200xx1.6xx9.1))` `=(66.25)/(53.96)`
`:.lamda_(2)=1.2278Å`
Now from equation (1),
`(P_(1))/(P_(2))=(1.2278)/(5000)`
`:.(P_(1))/(P_(2))=2.456xx10^(-4)`
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