1
MCQ (Single Correct Answer)

JEE Main 2018 (Online) 15th April Evening Slot

The de-Broglie's wavelength of electron present in first Bohr orbit of 'H' atom is :
A
0.529 $$\mathop {\rm A}\limits^ \circ $$
B
2$$\pi $$ $$ \times $$ 0.529 $$\mathop {\rm A}\limits^ \circ $$
C
$${{0.529} \over {2\pi }}$$ $$\mathop {\rm A}\limits^ \circ $$
D
4 $$ \times $$ 0.529 $$\mathop {\rm A}\limits^ \circ $$

Explanation

Radius    r = 0.529 $$ \times $$ $${{{n^2}} \over z}$$

In first Bohr orbit of hydrogen atom radius,

r = 0.529 $$ \times $$ $${{{1^2}} \over 1}$$ = 0.529 $$\mathop A\limits^ \circ $$

Angular momentum,

mvr = $${{nh} \over {2\pi }}$$

$$\therefore\,\,\,$$ for    n = 1,

    mvr = $${h \over {2\pi }}$$

$$ \Rightarrow $$$$\,\,\,$$ 2$$\pi $$r = $${h \over {mv}}$$ = $$\lambda $$   [ as   $$\lambda $$ = $${h \over {mv}}$$]

$$\therefore\,\,\,$$ $$\lambda $$ = 2$$\pi $$r = 2 $$\pi $$ $$ \times $$ 0.5 29
2
MCQ (Single Correct Answer)

JEE Main 2018 (Online) 16th April Morning Slot

Which of the following statements is false ?
A
Photon has momentum as well as wavelength.
B
Splitting of spectral lines in electrical field is called Stark effect.
C
Rydberg constant has unit of energy.
D
Frequency of emitted radiation from a black body goes from a lower wavelength to higher wavelength as the temperature increases.

Explanation

When a black body is heated, black body emit high energy radiation, from higher wavelength to lower wavelength.
3
MCQ (Single Correct Answer)

JEE Main 2019 (Online) 9th January Morning Slot

The highest value of the calculated spin- only magnetic moment (in BM) among all the transition metal complexes is :
A
5.92
B
6.93
C
3.87
D
4.90

Explanation

In transition metal contains d orbital, and in d orbital maximum no of unpaired electron possible = 5.

Spin only magnetic moment,

$${\mu _{spin}} = \sqrt {n\left( {n + 2} \right)} $$    B. M

here n $$=$$ Number of unpaired electrons.

$$ \therefore $$    $${\mu _{spin}} = \sqrt {5\left( {5 + 2} \right)} $$0    B. M

$$=$$ 5.92   B. M
4
MCQ (Single Correct Answer)

JEE Main 2019 (Online) 9th January Morning Slot

For emission line of atomic hydrogen from ni = 8 to nf = n, the plot of wave number $$\left( {\overline v } \right)$$ against $$\left( {{1 \over {{n^2}}}} \right)$$ will be (The Rydberg constant, RH is in wave number unit)
A
Linear with intercept $$-$$RH
B
Non linear
C
Linear with slope RH
D
Linear with slope $$-$$RH

Explanation

We know,

$$\overline v = {1 \over \lambda } = {R_H}{Z^2}\left[ {{1 \over {n_f^2}} - {1 \over {n_i^2}}} \right]$$

here ni $$=$$ 8 and nf $$=$$ n

Z $$=$$ 1 for hydrogen

$$ \therefore $$   $$\overline v = {1 \over \lambda } = {R_H}\left[ {{1 \over {{n^2}}} - {1 \over {{8^2}}}} \right]$$

So, graph is $$ \to $$



So, graph will be linear with slope RH.

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