## Question

In the Bohr model of the hydrogen atom, the ratio of the kinetic energy to the total energy of the electron in a quantum state *n* is

### Solution

–1

The total energy of electron bound to an atom is negative and is the sum of its P.E. and K.E. The magnitude of the P.E. is twice that of the K.E. (as per the Bohr model) but since the P.E. is – ve, we have

The total energy = (–2*K*) + (*K*) = –*K*

(*K* = Kinetic energy). Hence

total energy : kinetic energy = –1 : 1 = –1.

#### SIMILAR QUESTIONS

A hydrogen atom rises from its *n* = 1 state to the *n* = 4 state by absorbing energy. If the potential energy of the atom in *n* = 1 state be –13.6 eV, thencalculate : potential energy in *n* = 4 state.

The ionization energy of the hydrogen atom is given to be 13.6 eV. A photon falls on a hydrogen atom which is initially in the ground state and excites it to the *n* = 4 state. Calculate the wavelength of the photon.

An electron of energy 20 eV collides with a hydrogen atom in the ground state. As a result, the atom is excited to a higher energy state and the electron is scattered with reduced velocity. The atom subsequently returns to its ground state with emission of radiation of wavelength . Find the velocity of the scattered electron.

A proton captures a free electron whose kinetic energy is zero and forms a hydrogen atom of lowest energy-level (*n* = 1). If a photon is emitted in this process, what will be the wavelength of radiation? In which region of electromagnetic spectrum, will this radiation fall? (Ionisation potential of hydrogen atom = 13.6 V, ).

The de Broglie wavelength of a neutron at 927^{o}C is . What will be its wavelength at 27^{o}C?

What is the de Broglie wavelength of an electron of energy 1800 eV? Mass of electron and Planck’s constant .

Moving with the same velocity, which of the following has the longest de Broglie wavelength?

The de Broglie wavelength of an electron moving with a velocity is equal to that a photon. The ratio of the kinetic energy of the electron to that of the photon is

The distance of the closest approach of an alpha particle fired at a nuclear with momentum *p* is *r _{0}*. The distance of the closest approach when the alpha particle is fired at the same nucleus with momentum 2

*p*will be

The mass per nucleon in a heavy hydrogen atom is