Question

At what velocity does a proton have a 6.00-fm wavelength (about the size of a nucleus)? Assume the proton is nonrelativistic. (1 femtometer = (10⁻¹⁵ , {m}).)

a) (2.52 times 10⁶ , {m/s})
b) (4.88 times 10⁶ , {m/s})
c) (1.16 times 10⁷ , {m/s})
d) (8.21 times 10⁶ , {m/s})

Answer 1

To find the velocity of a proton with a 6.00-fm wavelength, use the formula velocity = Planck's constant / (wavelength × frequency). The correct answer is c) (1.16 × 10^7 m/s).

Step-by-step explanation:

To find the velocity of a proton with a 6.00-fm wavelength (about the size of a nucleus), we can use the formula:

velocity = wavelength × frequency

Since the proton is nonrelativistic, we can assume its velocity is much smaller than the speed of light. Thus, we can use the formula:

wavelength = Planck's constant / momentum

Combining these formulas, we get:

velocity = Planck's constant / (wavelength × frequency)

Using the given wavelength of 6.00 fm (or 6.00 × 10-15 m) and assuming the proton is nonrelativistic, we can calculate the velocity to be approximately 1.16 × 107 m/s. Therefore, the correct answer is c) (1.16 × 107 m/s).