Question 255: Atoms & Nuclei

Question

According to Bohr’s theory, the time averaged magnetic field at the centre (i.e. nucleus) of a hydrogen atom due to the motion of electrons in the n
th
orbit is proportional to : (n = principal  quantum number)

Accepted Answer

Magnetic field at the center of neucleus of H-atom
B = $${{{\mu _0}I} \over {2{r_n}}}$$
Radius of n
th
orbital,
r
n
= $${{{n^2}{h^2}{\varepsilon _0}} \over {m\pi Z{e^2}}}$$
$$	herefore\,\,\,$$  r
n
$$ \propto $$ n
2
velocity of electron in n
th
orbital,
$$\upsilon $$
n
= $$\left( {{{{e^2}h} \over {2{\varepsilon _0}}}} ight){Z \over n}$$
$$	herefore\,\,\,$$  $$\upsilon $$
n
$$ \propto $$ n
$$-$$1
I = $${q \over t}$$ = $${e \over {{{2\pi {r_n}} \over {{\upsilon _n}}}}}$$ = $${{e{\upsilon _n}} \over {2\pi {r_n}}}$$
$$	herefore\,\,\,$$ B = $${{{\mu _0}.\left( {{{e{\upsilon _n}} \over {2\pi {r_n}}}} ight)} \over {2{r_n}}}$$ = $${{{\mu _0}\,e{\upsilon _n}} \over {4\pi r_n^2}}$$
$$	herefore\,\,\,$$ B $$ \propto $$ $${{{\upsilon _n}} \over {r_n^2}}$$
$$ \Rightarrow $$ $$\,\,\,$$ B $$ \propto $$ $${{{n^{ - 1}}} \over {{n^4}}}$$
$$ \Rightarrow $$$$\,\,\,$$ B $$ \propto $$ n
$$-$$5

Answer

$${n^{ - 4}}$$

Answer

$${n^{ - 5}}$$

Answer

n
$$-$$3

Answer

n
$$-$$2

Atoms & Nuclei

According to Bohr’s theory, the time averaged magnetic field at the centre (i.e. nucleus) of a hydrogen atom due to the motion of electrons in the n th orbit is proportional to : (n = principal quantum number)

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