1- a- calculate the de broglie wavelength for a proton with a volacity 3.06% of

Question

1-
a- calculate the de broglie wavelength for a proton with a volacity 3.06% of the speed of light.

b- calculate the de broglie wavelength for a 5.20 oz baseball with a volacity of 96.0 mph

2-

calculate, to four significnat figures, the longest and shortest wavelengths of light emitted by electronsin the hydrogen atoms that begin in the n=8 state and then fall to state with smaller values of n

3-

consider the the ground state if zinc Zn .

a- how many electrons have / = 1 as one of their quantum numbers?
b- how many electrons have m/ = 0 ?
c- how many electrons have ms =+1?

Explanation / Answer

Here we need the equation for de Broglie that relates wavelength and particle speed:

= h /m

Where,

= wavelength

h = Planck’s constant (6.626 x 10-34 kg m2/s)

= velocity of the particle

m = mass of the particle (in this case the mass of proton: 1.672 x 10-27 kg)

We know that:

Speed of light = 3.00 x 108 m/s

So, the speed of the proton is equal to:

3.06 % / 100 % = 0.00306

0.00306 x (3.00 x 108 m/s) = 9.18 x 106 m/s

Putting values in equation:

=        6.626 x 10-34 kg m2/s

     (1.672 x 10-27 kg) x (9.18 x 106 m/s)

= 4.32 x 10-14 m

Converting meters in nanometers:

4.32 x 10-14 m (1 nm / 10-9 m) = 4.32 x 10-5 nm

We are going to calculate in a similar way that problem above.

We convert mph into m/s:

1 m/s = 2.237 mph

96.0 mph (1 m/s ÷ 2.237 mph) = 42.91 m/s

We convert ounces into kilograms:

1 oz = 0.0283495 kg

5.20 oz (0.0283495 kg / 1 oz) = 0.14742 kg

Here we need the equation for de Broglie that relates wavelength and particle speed:

= h /m

Where,

= wavelength

h = Planck’s constant (6.626 x 10-34 kg m2/s)

= velocity of the particle (42.91 m/s)

m = mass of the particle (in this case the mass of the baseball: 0.14742 kg)

=           6.626 x 10-34 kg m2/s

             (0.14742 kg) x (42.91 m/s)

= 1.05 x 10-34 m

Converting meters in nanometers:

1.05 x 10-34 m (1 nm / 10-9 m) = 1.05 x 10-25 nm

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