8. An electron in the ground state of the hydrogen atom moves at an average spee

Question

8. An electron in the ground state of the hydrogen atom moves at an average speed of 5x 100 m/s. If the speed is known to an uncertainty of 20%, what is the minimum uncertainty in its position? The mass of an electron is 9.1094 × 10 kg. A) 6x 10 11 m ma 31 B) 9×10.9 m C) 8 x 10-10 m D) 7 x 108 m E) 1 x 10-10 m 9. A proton has a mass of 1.67×10-27 kg. If the proton has wavelength of 3.97×10-10 m. What is its velocity as determined by the de Broglie equation? A) 1.00 × 103 m/s. B) 1.59 x 106 m/s C) 899 m/s. D) 108 m/s E) 605 m/s

Explanation / Answer

8)

Here:

velocity = 5*10^6 m/s

deltav = 20.0% of velocity

deltav = 20.0*5*10^6/100

deltav = 1*10^6 m/s

use Heisenberg uncertainty principle,

deltax*deltav = h/(4*pi*m)

Here:

deltav = 1*10^6 m/s

mass, m = 9.1094*10^-31 Kg

Putting values,

deltax*(1*10^6) = (6.626*10^-34)/(4*3.14*9.1094*10^-31)

deltax*(1*10^6) = 6*10^-5

deltax = 6*10^-11 m

Answer: A

Feel free to comment below if you have any doubts or if this answer do not work

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