1
MCQ (Single Correct Answer)

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

Radius of nth orbital,

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
MCQ (Single Correct Answer)

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
MCQ (Single Correct Answer)

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
MCQ (Single Correct Answer)

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

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