Atoms Test

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Atoms Test - 77

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Weekly Quiz Competition

Question 1
1 / -0

Choose the correct statements for hydrogen and deuterium atoms ( considering motion of nuclie as )

A
The radius of first Bohr orbit of deuterium is less than that of hydrogen

B
The speed of electron in the first Bohr orbit of deuterium is more than that of hydrogen.

C
The wavelength of first Balmer line of deuterium is more than that of hydrogen

D
The angular momentum of electron in the first Bohr orbit of deuterium is more than that of hydrogen.

Solution
Question 2
1 / -0

According to the Bohr's theory of hydrogen atom, the speed of the electron, its energy and the radius of its orbit varies with the principal quantum number n, respectively, as:

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

B
$$\dfrac { 1 }{ n } ,{ n }^{ 2 },\dfrac { 1 }{ { n }^{ 2 } } $$

C
$${ n }^{ 2 },\dfrac { 1 }{ { n }^{ 2 } } ,{ n }^{ 2 }$$

D
$$n,\dfrac { 1 }{ n } ,\dfrac { 1 }{ { n }^{ 2 } } $$

Solution
Question 3
1 / -0

In Rutherford experiments on $$\alpha$$- ray scattering the number of particles scattered at $${90}^{o}$$ be $$28$$ per minute. Then the number of particles scattered per minute by the same foil, but at $${60}^{o}$$ is

A
$$56$$

B
$$112$$

C
$$60$$

D
$$120$$
Question 4
1 / -0

If the radius of Bohr's second orbit of hydrogen atom is $$\alpha$$ then the radius of the $$4^{th}$$ Bohr orbit in atom with Z=3, is

A
$$\cfrac {4\alpha}3$$

B
$$\cfrac {16\alpha}3$$

C
$$\cfrac {\alpha}4$$

D
None of these

Solution
Question 5
1 / -0

Hydrogen atom is excited from ground state to another state with principal quantum number equal to $$4$$. Then the number of spectral lines in the emission spectra will be :

A
$$6$$

B
$$2$$

C
$$3$$

D
$$5$$

Solution
Question 6
1 / -0

The radius of the first orbit of hydrogen atom is equal to the radius of the

A
first orbit of $$He^{ + }$$

B
second orbit of $${ Be }^{ 3+ }$$

C
fourth orbit of $$He^{ + }$$

D
third orbit of $${ Be }^{ 3+ }$$

Solution
Question 7
1 / -0

Suppose an electron is attracted towards the origin by a force $$k/r$$ where $$'k'$$ is a constant and $$'r'$$ is the distance of the electron from the origin. By applying Bohr model to this system, the radius of the $$nth$$ orbital of the electron is found to be $$'rn'$$ and the kinetic energy of the electron to be $$Tn$$. Then which of the following is true?

A
$$T_{n} \propto 1/n^{2}, r_{n}\propto n^{2}$$

B
$$T_{n}$$ independent of $$n, r_{n} \propto n$$

C
$$T_{n} \propto 1/n, r_{n}\propto n$$

D
$$T_{n} \propto 1/n, r_{n} \propto n^{2}$$

Solution
Question 8
1 / -0

A particle of mass $$m$$ moves in a circular orbit in a central potential field $$U(r)=\dfrac { 1 }{ 2 } kr^2$$. If Bohr's quantization condition is applied, radii of possible orbitals and energy levels vary with quantum number $$n$$ as:

A
$$r_n \propto n^2, E_n \propto \dfrac { 1}{n^2 }$$

B
$$r_n \propto \sqrt { n } , E_n \propto \dfrac { 1}{n }$$

C
$$r_n \propto n, E_n \propto n$$

D
$$r_n \propto \sqrt { n } , E_n \propto n$$

Solution

$$F=\frac { dV}{ dR } =kr=\frac { mv^2}{ r } $$
$$mvr=\frac { nh}{ 2\pi }$$
$$r^2\infty n$$
$$r^2\infty \sqrt {n }$$
$$E=\frac { 1}{ 2 } kr^2+\frac { 1}{ 2 } mv^2\infty r^2$$
Question 9
1 / -0

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

A
$$60$$

B
$$32$$

C
$$4$$

D
$$64$$
Question 10
1 / -0

A certain dye absorbs light of $$\lambda =4000\overset { \circ }{ A } $$ and emits fluorescent light of $$\lambda =5000\overset { \circ }{ A } $$. Assuming that under given condition 50% of the absorbed energy is re-emitted out fluorescence, Calculate the ratio of the number of quanta emitted out to the number of quanta absorbed :

A
$$\dfrac { 5 }{ 8 } $$

B
$$\dfrac { 8 }{ 5 } $$

C
$$\dfrac { 3 }{ 8 } $$

D
$$\dfrac { 8 }{ 3 } $$

Solution