Calculate the frequency of revolution of electron in the second Bohr's orbit of radius 2.12A . Given h=6.6×10^-34 Js , m = 9.1×10^-31 kg?

Question

Answer

Calculation of Electron's Frequency of Revolution in Second Bohr's Orbit

Bohr's model of an atom states that electrons revolve around the nucleus in certain fixed orbits. The frequency of revolution of an electron in these orbits can be calculated using the formula:

f = v / 2πr

where,

f is the frequency of revolution

v is the velocity of the electron

r is the radius of the orbit

Calculation of Velocity of Electron

The velocity of the electron can be calculated using the formula:

v = (nh) / 2πmr

where,

n is the principal quantum number of the orbit (here, n = 2)

h is Planck's constant (given as 6.6×10^-34 Js)

m is the mass of the electron (given as 9.1×10^-31 kg)

r is the radius of the orbit (given as 2.12A = 2.12×10^-10 m)

Substituting these values, we get:

v = (2×6.6×10^-34) / (2×3.14×9.1×10^-31×2.12×10^-10) = 2.2×10^6 m/s

Calculation of Frequency of Revolution

Substituting the value of velocity and radius in the formula for frequency of revolution, we get:

f = (2.2×10^6) / (2×3.14×2.12×10^-10) = 1.6×10^15 Hz

Explanation

The Bohr's model of an atom is a simplified representation of the atomic structure. According to this model, electrons revolve around the nucleus in certain fixed orbits. These orbits are characterized by their principal quantum number, which determines the energy of the electron in that orbit. The radius of the orbit is also determined by this quantum number, and the velocity of the electron can be calculated using the formula mentioned above.

The frequency of revolution of an electron in a particular orbit can be calculated using the velocity and radius of the orbit. This frequency represents the number of complete revolutions made by the electron in one second. In the present case, we have calculated the frequency of revolution of an electron in the second Bohr's orbit of radius 2.12A. We have used the values of Planck's constant and the mass of the electron to calculate the velocity of the electron and then used this value to calculate the frequency of revolution.

Answer

Mvr = nh/2π

=> m(rω)r = nh/2π

=> mr²ω = nh/2π

NOW SUBSTITUTE THE VALUES AND GET THE ANSWER 👍👍👍👍👍👍👍

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