Kinetic Energy of an Electron in the Second Bohr Orbit of Hydrogen Atom

The Bohr model of the hydrogen atom was proposed by Niels Bohr in 1913, which described the structure of the atom and the way electrons occupy different energy levels. The second Bohr orbit is the second energy level of the hydrogen atom, where the electron is more energetic than in the first orbit.

Formula for calculating Kinetic Energy

The formula for calculating kinetic energy is 1/2mv^2, where m is the mass of the object and v is its velocity. In the case of an electron in the second Bohr orbit of hydrogen atom, the mass is the mass of an electron, which is 9.10938356 × 10^-31 kilograms.

Velocity of an Electron in the Second Bohr Orbit

The velocity of an electron in the second Bohr orbit of hydrogen atom can be calculated using the formula v = (Zke^2)/2rh, where Z is the atomic number of the atom, k is Coulomb's constant, e is the charge of an electron, and rh is the radius of the second Bohr orbit. For the hydrogen atom, Z is 1, k is 8.9875517923 × 10^9 N·m^2/C^2, e is 1.602176634 × 10^-19 C, and rh is 5.29177210903 × 10^-11 meters.

Calculation of Kinetic Energy

Substituting the values in the formula for velocity, we get v = (1.44 × 10^8 m/s). Using the formula for kinetic energy, we get KE = 1/2(9.10938356 × 10^-31 kg)(1.44 × 10^8 m/s)^2, which gives us a value of 1.04 × 10^-18 joules.

Therefore, the kinetic energy of an electron in the second Bohr orbit of hydrogen atom is 1.04 × 10^-18 joules.