## Question

A microscope using suitable photons is employed to locate an electron in an atom within a distance of 0.1 Å. What is the uncertainty involved in the measurement of its velocity?

### Solution

Here, we are given

Applying uncertainty principle,

.

#### SIMILAR QUESTIONS

Calculate the wavelength of the spectral line obtained in the spectrum of Li^{2+} ion when the transition takes place between two levels whose sum is 4 and the difference is 2.

Calculate the wavelength of the radiation emitted when an electron in a hydrogen atom undergoes a transition from 4th energy level to the 2nd energy level. In which part of the electromagnetic spectrum does this line lie?

Calculate the velocity of electron in the first Bohr orbit of hydrogen atom. Given that

Bohr radius = 0.529 Å,

Planck’s constant, *h* = 6.626 × 10^{–34} Js,

mass of electron = 9.11 × 10^{–31} kg and

1 J = 1 kg m^{2}s^{–2}.

Calculate ionization energy of the hydrogen atom.

The ionisation energy of He^{+} is . Calculate the energy of first stationary state of Li^{2+}.

The ionization energy of hydrogen in excited state is +0.85 eV. What will be the energy of the photon emitted when it returns to the ground state?

Calculate the wavelength associated with an electron

(mass 9.1 × 10^{–31} kg) moving with a velocity of 10^{3} m sec^{–1}

(*h* = 6.6 × 10^{–34} kg m^{2} sec^{–1})

What will be the wavelength of a ball of mass 0.1 kg moving with a velocity of 10 ms^{–1}?

Calculate the mass of a photon with wavelength 3.6 Å.

Calculate the uncertainty in the velocity of a wagon of mass 3000 kg whose position is known to an accuracy of ±10 pm

(Planck’s constant = 6.63 × 10^{–34} Js)