Let `v_n and E_n` be the respective speed and energy of an electron in the n-th orbit radius `r_n` in a hydrogen atom, as predicted by Bohr's model . Then
A
plot of `E_(n)r_(n)//E_(1)r_(1)` as a function of n is a straight line of slope 0.
B
plot of `r_(n)v_(n)//r_(1)v_(1)` as a function of n is a straight line of slope 1.
C
plot of `ln(r_(n)/r_(1))` as a function of ln(n) is a straight line of slope 2.
D
plot of `ln((r_(n)E_(1))/(E_(n)r_(1)))` as a function of ln(n) is a straight line of slope 4.
Text Solution
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The correct Answer is:
A, B, C, D
The speed of an electron, `v_(n)=v_(1)/n` The energy of an electron, `E_(n)=E_(1)/n_(2)` The radius of electron, `r_(n)=n^(2)r_(1)` `therefore E_(n)r_(n)=E_(1)/n^(2).r_(1)n^(2)=E_(1)r_(1)" or (E_(n)r_(n))/(E_(1)r_(1))=1` Hence, option (a) is correct. `therefore r_(n)v_(n)=n^(2)r_(1)""v_(1)/n=nv_(1)r_(1)" or "(r_(n)v_(n))/(r_(1)v_(1))=n` Hence, option (b) is correct. `therefore r_(n)/r_(1)=n^(2)" or "In(r_(n)/r_(1))=2In(n)` Hence, option (c) is correct. `therefore r_(n)/E_(n)=(n^(2)r_(1))/(E_(1)//n^(2)) rArr (r_(n)E_(1))/(E_(n)r_(1))=n^(4)` or `In((r_(n)E_(1))/(E_(n)r_(1)))=4In(n)` Hence, option (d) is correct.
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