Question 10

In accordance with the Bohr’s model, find the quantum number that characterises the earth’s revolution around the sun in an orbit of radius 1.5 × 10^{11} m with orbital speed 3 × 10^{4} m/s. (Mass of earth = 6.0 × 10^{24} kg.)

Answer

Radius of the orbit of the Earth around the Sun, r = 1.5 × 10^{11} m

Orbital speed of the Earth, ν = 3 × 10^{4} m/s

Mass of the Earth, m = 6.0 × 10^{24} kg

According to Bohr’s model, angular momentum is quantized and given as:

mvr = nh/2π

Where,

h = Planck’s constant = 6.62 × 10^{−34} Js

n = Quantum number

∴ n = mvr2π/h

= (2πx6x10^{24}x3x10^{4}x1.5x10^{11})/(6.62x10^{-34})

= 25.61x10^{73} = 2.6 x 10^{74}

Hence, the quanta number that characterizes the Earth’ revolution is 2.6 × 10^{74} .

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- Q:-
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A point charge of 2.0 μC is at the centre of a cubic Gaussian surface 9.0 cm on edge. What is the net electric flux through the surface?

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A 12 pF capacitor is connected to a 50V battery. How much electrostatic energy is stored in the capacitor?

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Two tiny spheres carrying charges 1.5 μC and 2.5 μC are located 30 cm apart. Find the potential and electric field:

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A system has two charges q

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(b) If the net outward flux through the surface of the box were zero, could you conclude that there were no charges inside the box? Why or Why not?

- Q:-
Consider a uniform electric field E = 3 × 10

^{3}îN/C.(a) What is the flux of this field through a square of 10 cm on a side whose plane is parallel to the yz plane?

(b) What is the flux through the same square if the normal to its plane makes a 60° angle with the x-axis?

- Q:-
A conducting sphere of radius 10 cm has an unknown charge. If the electric field 20 cm from the centre of the sphere is 1.5 × 10

^{3}N/C and points radially inward, what is the net charge on the sphere? - Q:-
A charge of 8 mC is located at the origin. Calculate the work done in taking a small charge of -2 x 10

^{-9}C from a point P (0, 0, 3 cm) to a point Q (0, 4 cm, 0), via a point R (0, 6 cm, 9 cm). - Q:-
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