1

### JEE Main 2017 (Online) 8th April Morning Slot

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 nth orbit is proportional to : (n = principal quantum number)
A
${n^{ - 4}}$
B
${n^{ - 5}}$
C
n$-$3
D
n$-$2

## Explanation

Magnetic field at the center of neucleus of H-atom

B = ${{{\mu _0}I} \over {2{r_n}}}$

rn = ${{{n^2}{h^2}{\varepsilon _0}} \over {m\pi Z{e^2}}}$

$\therefore\,\,\,$ rn $\propto$ n2

velocity of electron in nth orbital,

$\upsilon$n = $\left( {{{{e^2}h} \over {2{\varepsilon _0}}}} \right){Z \over n}$

$\therefore\,\,\,$ $\upsilon$n $\propto$ n$-$1

I = ${q \over t}$ = ${e \over {{{2\pi {r_n}} \over {{\upsilon _n}}}}}$ = ${{e{\upsilon _n}} \over {2\pi {r_n}}}$

$\therefore\,\,\,$ B = ${{{\mu _0}.\left( {{{e{\upsilon _n}} \over {2\pi {r_n}}}} \right)} \over {2{r_n}}}$ = ${{{\mu _0}\,e{\upsilon _n}} \over {4\pi r_n^2}}$

$\therefore\,\,\,$ B $\propto$ ${{{\upsilon _n}} \over {r_n^2}}$

$\Rightarrow$ $\,\,\,$ B $\propto$ ${{{n^{ - 1}}} \over {{n^4}}}$

$\Rightarrow$$\,\,\,$ B $\propto$ n $-$5
2

### JEE Main 2017 (Online) 8th April Morning Slot

Two deuterons undergo nuclear fusion to form a Helium nucleus. Energy released in this process is : (given binding energy per nucleon for deuteron = 1.1 MeV and for helium = 7.0 MeV)
A
30.2 MeV
B
32.4 MeV
C
23.6 MeV
D
25.8 MeV

## Explanation

1H2 + 1H2  $\to$  2He4

No. of proton in one dueteron = 2

$\therefore\,\,\,$ Total protons in two dueterons = 2 $\times$ 2 = 4

$\therefore\,\,\,$ Binding energy of two dueteron

= 1.1 $\times$ 4 = 4 : 4 MeV

In (2He4) no of protons = 4

$\therefore\,\,\,$ Binding energy of (2He4) nuclei = 4 $\times$ 7 = 28 Mev

Energy released in this process = 28 $-$ 4.4 = 23.6 MeV
3

### JEE Main 2017 (Online) 9th April Morning Slot

The acceleration of an electron in the first orbit of the hydrogen atom (n = 1) is :
A
${{{h^2}} \over {{\pi ^2}{m^2}{r^3}}}$
B
${{{h^2}} \over {{8\pi ^2}{m^2}{r^3}}}$
C
${{{h^2}} \over {{4\pi ^2}{m^2}{r^3}}}$
D
${{{h^2}} \over {{4\pi }{m^2}{r^3}}}$
4

### JEE Main 2017 (Online) 9th April Morning Slot

Imagine that a reactor converts all given mass into energy and that it operates at a power level of 109 watt. The mass of the fuel consumed per hour in the reactor will be : (velocity of light, c is 3×108 m/s)
A
0.96 gm
B
0.8 gm
C
4 $\times$ 10$-$2 gm
D
6.6 $\times$ 10$-$5 gm