Data: Speed of light = 2.998-10^8 ms^-1; mass of electron 9.109 10^-31kg; Planck
ID: 965368 • Letter: D
Question
Data: Speed of light = 2.998-10^8 ms^-1; mass of electron 9.109 10^-31kg; Planck's constant = 6.626 10^-34 J s; Avogadro's number = 6.022 10^23 mol^-1 Electromagnetic wave A represents infrared light and electromagnetic wave B represents visible light. Compared with electromagnetic wave B, electromagnetic wave A has (a higher/a lower/the same) frequency and (a longer/a shorter/the same) wavelength. A photon has energy of 3.55 10^-19 J. The wavelength of this light is: 1.87 10^-15 m 2.04 10^-15 m 3.34 10^-9 m 5.60 10^-7 m 6.11 10^-7 m 6.53 10^-4 m 7.13 10^-4 m None of the above. The correct wavelength is m. An electron moves at a speed of 5.41 Times 10^6 m s^-1. The wavelength of the electron is: 1.93 10^-13 m 2.43 10^-12 m 1.07 10^-11 mExplanation / Answer
2) energy of photon E = (h·c) /
h = planck's constant , C = speed of light , = wavelength
3.55 x 10-19 J = (6.626 x 10-34 x 2.998 x 108) /
= (6.626 x 10-34 x 2.998 x 108) / 3.55 x 10-19 J
= 5.5957 x 10-7 m = 5.60 x10-7 M
3) The first step in the solution is to calculate the kinetic energy of the electron:
KE = (1/2)mv2 { mass = 9.11 x 10¯31 kg}
x = (1/2) (9.11 x 10¯31 kg) (5.41 x 106 m/s)2
x = 1.3331 x 10¯17 kg m2 s¯2 (I kept some guard digits)
When I use this value just below, I will use J (for Joules).
Next, we will use the de Broglie equation to calculate the wavelength:
= h/p
= h /(2Em)
x = 6.626 x 10¯34 J s / [(2) (1.3331 x 10¯17 J) (9.11 x 10¯31 kg)]
Just to be sure about two things: (1) the unit on Planck's Constant is Joule-seconds, both are in the numerator and (2) there are three values following the radical in the denominator. All three of them are under the radical sign.
The answer:
x = 1.344 x 10¯10 m
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