To resolve an object in an electron microscope, the wavelength of the electrons must be close to the diameter of the object. What kinetic energy, E k , must the electrons have in order to resolve a protein molecule that is 2.70 nm in diameter? Take the mass of an electron to be 9.11 × 10 − 31 kg .

KE = 3.308×10^-20J

Explanation:

Let the wavelength of the electron equal the diametre of the protein molecule

Wavelength = 2.70 nm = 2.70 × 10^-7m

The de Brogule expression gives ud:

Wavelength = h/ mv

V = h/m × wavelength

Where h is plank's constant

V = (6.63×10^-11)/(9.11×10^-31)(2.70×10^-9)

V = (6.63×10^-34)/(2.4587×10^-30)

V = 2.695×10^5m/s

KE = 1/2mv^2

KE = 1/2 (9.11×10^-31)( 2.695 ×10^5)^2

KE = 1/2 ×(9.11×10^-31)(7.26×10^10)

KE = 3.308×10^-20J

3.32 * 10^-20 J

Explanation:

Let the wavelength of the electron be equal to the diameter if the protein molecule.

λ = 2.7 * 10 ^ -9 m

using De Broglie's equation

λ= h / mv

Where

λ= wavelength

h= Planck's constant

m= mass of the particle

v= velocity of movement of the particle

Then...

v = h / mλ

v = (6.63 * 10^-34) / [(9.11 * 10^-31) * (2.7 * 10^-9)]

v = 2.70 * 10^5 m/s

KE = Kinetic Energy

KE = 1/2mv²

KE = 1/2 (9.11 * 10^-31) * (2.7 * 10^5)²

KE = 3.32 * 10^-20 J

search it up!

explanation:

scattering of light by tiny particles in air to produce the colors we see on sky, is dependent on the following factors:

(i) wavelength of light

(ii) size of the scattering particle  

(iii) distance traveled by light through the atmosphere.

according to rayleigh's law of scattering, the amount of scattering is inversely proportional to the fourth power of its wavelength. shorter the wavelength, greater is its scattering. hence violet/blue light is scattered more than red.

sun's light is a composite light ( visible light) with wavelengths in the range 400 nm (violet) to 700 nm (red). as sunlight passes through our atmosphere, the molecules of air scatter light according to their wavelengths. during sunrise and sunset, the sun's position is below the horizon. hence light from the sun travels a greater distance in the atmosphere when compared to its position a noon.

as sunlight enters the earth's atmosphere, blue light is scattered away and at the end of its journey in the sky, only red and orange wavelengths remain in the beam.

hence at sunrise and sunset, the sky appears reddish orange.