Atoms Test

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Atoms Test - 48

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Weekly Quiz Competition

Question 1
1 / -0

A single electron orbits around a stationary nucleus of charge $$+Ze$$, where $$Z$$ is a constant and $$e$$ is the magnitude of the electronic charge. It required $$47.2\ eV$$ to excite the electron from the second Bohr orbit to the third Bohr orbit. Find the value of $$Z$$.

A
$$z = 5$$.

B
$$z = 6$$.

C
$$z = 8$$.

D
$$z = 2$$.

Solution
Question 2
1 / -0

The total energy of in the electron in the hydrogen atom in the ground state is $$-13.6\ eV$$. Which of the following is its kinetic energy in the first exited state?

A
$$13.6 \ eV$$

B
$$6.8 \ eV$$

C
$$3.4 \ eV$$

D
$$1.825 \ eV$$

Solution

Energy nth orbit of hydrogen atom is given by,

$$E_n=\dfrac{-13.6}{n^2}e.V$$

For ground state, $$n=1$$

$$\therefore E_l=\dfrac{-13.6}{l^2}=-13.6eV$$

for first excited state, $$n=2$$

$$\therefore E_2=\dfrac{-136.6}{2^2}=\dfrac{-136.6}{4}=-3.4eV$$

Kinetic energy of an electron in the first excited state is,

$$K.E=-E_2$$

$$\Rightarrow K.E=3.4eV$$
Question 3
1 / -0

If the attractive potential between electron and proton were given by $$V(r) = V_{0}ln \left (\dfrac {r}{r_{0}}\right )$$ (where $$V_{0}, r_{0}$$ are constants), the radius $$r_{n}$$ of the $$nth$$ Bohr orbit in Hydrogen atom would be proportional to

A
$$n^{2}$$

B
$$n$$

C
$$1/n$$

D
$$1/n^{2}$$

Solution

$$V_{(r)} = V_0 \ln \left(\dfrac{r}{r_0} \right)_{nth}$$
$$r_n \alpha ?$$
$$r_n =$$ radius of both orbit in $$H-$$ atom
$$F = -\dfrac{dv}{dr} = \dfrac{mv^2}{r}$$
$$v = \sqrt{\dfrac{Fr}{m}}$$
and $$mv_n \ln = \dfrac{nh}{2 \pi} $$ (angular momentum)
$$\ln \, 2n$$
Question 4
1 / -0

If element with principal quantum number $$n > 4$$ were not allowed in nature, the number of possible elements would be

A
$$60$$

B
$$32$$

C
$$4$$

D
$$64$$

Solution

If the element with principal quantum
number$$n>4$$
when $$n=4$$
The formula becomes$$=2(4)^2\\=16\times2\\=32$$
When $$n=5$$
The formula becomes$$=2(5)^2$$
Hence the number of elements would$$=60$$
Question 5
1 / -0

A single electron orbits around a stationary nucleus of charge $$+Ze$$, where $$Z$$ is a constant and $$e$$ is the magnitude of the electronic charge. It required $$47.2\ eV$$ to excite the electron from the second Bohr orbit to the third Bohr orbit.
Find The wavelength of the electromagnetic radiation required to remove the electron from the first Bohr orbit.

A
$$36.4$$

B
$$53$$

C
$$40$$

D
$$66$$

Solution
Question 6
1 / -0

The number of waves in the third orbit of H atom is

A
1

B
2

C
4

D
3

Solution

No of waves= Shell No of the orbit= 3
Question 7
1 / -0

The radius of the first Bohr orbit is $$a_{0}$$. The $$n^{th}$$ orbit has a radius:

A
$$na_{0}$$

B
$$a_{0}/n$$

C
$$n^{2}a_{0}$$

D
$$a_{0}/n^{2}$$

Solution

Radius of $$n^{th}$$ orbital
$$r_n=\dfrac{\epsilon_0n^{2}h^{2}}{\pi mZe^2}$$
Wherein
$$=r_n\propto\dfrac{n^2}{Z}$$

$$=\dfrac{\epsilon_0h^{2}}{\pi me^2}=0.529$$

$$r=\dfrac{n^2}{Z}a_0$$

For $$Z=1$$ $$r=n^{2}a_0$$
Question 8
1 / -0

The average current due to an electron orbiting the proton in the $$n^{th}$$ Bohr orbit of the hydrogen atom is

A
$$\propto n$$

B
$$\propto n^{3}$$

C
$$\propto n^{-3}$$

D
none of these

Solution

We know,
$$r_n \propto \dfrac{1}{n^2}$$

$$v_n \propto \dfrac{Z}{n}$$

$$\omega=\dfrac{2\pi r_n}{v_n}$$

$$\omega\propto\dfrac{Z}{n^3}$$

$$I\propto\omega\propto\dfrac{1}{n^{-3}}$$

$$L\propto n^{-3}$$

Hence option $$\textbf C $$ is correct.
Question 9
1 / -0

The ionisation potential of a hydrogen atom is $$13.6\ volt$$. The energy required to remove an electron from the second orbit of hydrogen is:

A
$$3.4\ eV$$

B
$$6.8\ eV$$

C
$$13.6\ eV$$

D
$$27.2\ eV$$

Solution

Energy required to remove electron in the $$n=2$$ state

$$E_n=-13.6\dfrac{Z^2}{n^2}$$

$$\Delta E=-13.6\left[\dfrac{1}{\infty^2}-\dfrac{1}{4}\right]$$

$$\Delta E=\dfrac{13.6}{4}eV$$

$$=3.4\ eV$$
Question 10
1 / -0

The radius of the shortest orbit in a one-electron system is $$18\ pm$$. It may be

A
Hydrogen

B
Deuterium

C
$$He^{+}$$

D
$$Li^{2+}$$

Solution

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Re-Attempt Weekly Quiz Competition

Atoms Test - 48

Result

Atoms Test - 48

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SHARING IS CARING

Question 1

$$z = 5$$.

$$z = 6$$.

$$z = 8$$.

$$z = 2$$.

Solution

Question 2

$$13.6 \ eV$$

$$6.8 \ eV$$

$$3.4 \ eV$$

$$1.825 \ eV$$

Solution

Question 3

$$n^{2}$$

$$n$$

$$1/n$$

$$1/n^{2}$$

Solution

Question 4

$$60$$

$$32$$

$$4$$

$$64$$

Solution

Question 5

$$36.4$$

$$53$$

$$40$$

$$66$$

Solution

Question 6

1

2

4

3

Solution

Question 7

$$na_{0}$$

$$a_{0}/n$$

$$n^{2}a_{0}$$

$$a_{0}/n^{2}$$

Solution

Question 8

$$\propto n$$

$$\propto n^{3}$$

$$\propto n^{-3}$$

none of these

Solution

Question 9

$$3.4\ eV$$

$$6.8\ eV$$

$$13.6\ eV$$

$$27.2\ eV$$

Solution

Question 10

Hydrogen

Deuterium

$$He^{+}$$

$$Li^{2+}$$

Solution

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