Protons can be accelerated to speeds near the speed of light in particle accelerators. Calculate the wavelength of a proton moving at 2.90 x 108 m/s if the proton was a mass of 1.673 x 10-24 g. 2. Give the values for the quantum numbers associated with the following orbitals a) 2p b) 3s c) 5d

(1) The wavelength of the proton is 1.366 x 10⁻¹⁵ m

(2) 2p( l = 1, ml = -1,0,+1)

    3s( n = 3, l = 0, ml = 0)

    5d ( l = 2, ml = -2,-1,0,+1,+2)

Explanation:

Given;

mass of the proton; m = 1.673 x 10⁻²⁴ g = 1.673 x 10⁻²⁷ kg

velocity of the proton, v = 2.9 x 10⁸ m/s

The wavelength of the proton is calculated by applying De Broglie's equation;

where;

h is Planck's constant = 6.626 x 10⁻³⁴ J/s

Substitute the given values and solve for wavelength of the proton;

(2) the values for the quantum numbers associated with the following orbitals is given by;

n, which represents Principal Quantum number

which represents Azimuthal Quantum number

which represents Magnetic Quantum number

(a) 2p (number of orbital = 3):

(b) 3s (number of orbital = 1):

(c) 5d (number of orbital = 5)