Atoms Test

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Atoms Test - 59

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Weekly Quiz Competition

Question 1
1 / -0

According to Bohr hydrogen atom model the radius of stationary orbit directly proportional to principal quantum number n as $$\rightarrow $$

A
$$\dfrac { 1 }{2 n } $$

B
$$n^2$$

C
$${ n } $$

D
none of these

Solution
Question 2
1 / -0

The nuclear radius of a certain nucleus is $$7.2 f m $$ and it has a charge of $$1.28 \times 10 ^ { - 17 } { C }.$$ The number of neutrons inside the nucleus is

A
$$136$$

B
$$140$$

C
$$126$$

D
$$142$$

Solution

$$\begin{array}{l} { n_{ p } }+{ n_{ p } } \\ A={ \left( { \frac { r }{ { { r_{ o } } } } } \right) ^{ 3 } } \\ ={ \left( { \frac { { 7.2 } }{ { 1.2 } } } \right) ^{ 3 } }={ 6^{ 3 } }=216 \\ { x_{ p } }=\frac { q }{ e } =\frac { { 1.28\times { { 10 }^{ -17 } } } }{ { 1.6\times { { 10 }^{ -19 } } } } =80 \\ \therefore \, \, { n_{ p } }=216-80=136 \end{array}$$
Question 3
1 / -0

The ratio of the kinetic energy to the total energy of an electron in a Bohr orbit is

A
$$1:-1$$

B
$$2$$

C
$$1 : 2$$

D
$$None$$

Solution

$$k =kinetic\, energy$$
$$E=total\, energy$$
$$K=-E$$
$$\dfrac{K}{E}=\dfrac{1}{-1}$$
Question 4
1 / -0

According to Bohr's hypothesis , the angular momentum of the electron on any stationary orbit of radius r is proportional to ......

A
independent of r

B
1/r

C
$$ \sqrt r $$

D
$$ r^2 $$

Solution

We know, there will be two forces acting, electrostatic and centripetal force; so

$$F_{c}=F_{e} \\$$
$$\frac{m v^{2}}{r}=\frac{1}{4 \pi \varepsilon_{0}} x \frac{e^{2}}{r^{2}} \\$$
$$v^{2}=\frac{1}{4 \pi \varepsilon_{0}} \frac{e^{2}}{m r} \\$$
$$V=\frac{e^{2}}{4 \pi \varepsilon_{0} r}$$

We know, $$r_{n} \propto \frac{n^{2}}{2}$$

$$n=(z r)^{1 / 2} \\$$
$$L=\frac{n h}{2 \pi} \times n \times(22)^{1 / 2}$$

$$\therefore \quad L \alpha \sqrt{r}$$
(c) $$\sqrt{2}$$
Question 5
1 / -0

An electron of H-atom de-excites from energy level $$n_1=2$$ to $$n_2=1$$ and the emitted photon is incident on $$He^+$$ ions in ground and first excited state. Which of following transition is possible.

A
$$n=1$$ to $$n=4$$

B
$$n=2$$ to $$n=4$$

C
$$n=2$$ to $$n=3$$

D
$$n=1$$ to $$n=3$$

Solution

$$E=13.6\times 1(\dfrac { 1 }{ 1^{ 2 } } -\dfrac { 1 }{ 2^ 2 })$$
$$\Rightarrow10.2eV $$

for He+in $$n=2$$
$$10.2eV=13.6\times4(\dfrac { 1 }{ 2^{ 2 } } -\dfrac { 1 }{ n^ 2 } )$$
$$\Rightarrow n=4$$
Question 6
1 / -0

Find the average of radius for $$A{u^{197}}$$.

A
$$6.4\;{\text{fm}}$$

B
$$4.6\;{\text{fm}}$$

C
$$0.46\;{\text{fm}}$$

D
None of these
Question 7
1 / -0

The size of an atom is of the order of

A
$$ 10^{-8} m $$

B
$$ 10^{-10} m $$

C
$$ 10^{-12} m $$

D
$$ 10^{-14} m $$

Solution
Question 8
1 / -0

The energy level diagram for an hydrogen like atom is shown in the figure.The radius of its first Bohr orbit is
0 eV ____________n = $$\infty $$
-6.04 eV __________ n = 3
-13.6 eV ____________ n =2
-54.4 eV ____________ n=1

A
$$ 0.265 \mathring { A } $$

B
$$ 0.53 \mathring { A } $$

C
$$ 0.132 \mathring { A } $$

D
None of these

Solution

We know that $$E_n=-13.6 \dfrac{Z^2}{n^2}eV$$ and $$r_n=0.53 \dfrac{n^2}{Z}(A^o)$$

Here for $$n=1,\ E=-54.4\ eV$$

Therefore $$-54.4=-13.6 \dfrac{Z^2}{1^1} \Rightarrow Z=2$$

hence radius of first orbit $$r=\dfrac{0.53(1)^2}{2}=0.265\ A^o$$
Question 9
1 / -0

If $$ '\lambda ' $$ the longest wavelength of Lyman series, then shortest wavelength line that of the Balmer series is:-

A
$$ 5 \lambda $$

B
$$ 2 \lambda $$

C
$$ 4 \lambda $$

D
$$ 3 \lambda $$
Question 10
1 / -0

According to Bohr's theory, the product of velocity of electron in $$ n^{th} $$ orbit and the radius of $$ n^{th} $$ orbit is:

A
inversely proportional to the mass of the electron

B
directly proportional to the mass of the electron

C
independent of the mass of the electron

D
directly proportional to the square of mass of the electron

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Re-Attempt Weekly Quiz Competition

Atoms Test - 59

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Atoms Test - 59

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SHARING IS CARING

Question 1

$$\dfrac { 1 }{2 n } $$

$$n^2$$

$${ n } $$

none of these

Solution

Question 2

$$136$$

$$140$$

$$126$$

$$142$$

Solution

Question 3

$$1:-1$$

$$2$$

$$1 : 2$$

$$None$$

Solution

Question 4

independent of r

1/r

$$ \sqrt r $$

$$ r^2 $$

Solution

Question 5

$$n=1$$ to $$n=4$$

$$n=2$$ to $$n=4$$

$$n=2$$ to $$n=3$$

$$n=1$$ to $$n=3$$

Solution

Question 6

$$6.4\;{\text{fm}}$$

$$4.6\;{\text{fm}}$$

$$0.46\;{\text{fm}}$$

None of these

Question 7

$$ 10^{-8} m $$

$$ 10^{-10} m $$

$$ 10^{-12} m $$

$$ 10^{-14} m $$

Solution

Question 8

$$ 0.265 \mathring { A } $$

$$ 0.53 \mathring { A } $$

$$ 0.132 \mathring { A } $$

None of these

Solution

Question 9

$$ 5 \lambda $$

$$ 2 \lambda $$

$$ 4 \lambda $$

$$ 3 \lambda $$

Question 10

inversely proportional to the mass of the electron

directly proportional to the mass of the electron

independent of the mass of the electron

directly proportional to the square of mass of the electron

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