The Radius of a Typical Nucleus Is About $5 \times 10 ^ { - 15 } \mathrm {~m}$

Multiple Choice

The radius of a typical nucleus is about $5 \times 10 ^ { - 15 } \mathrm {~m}$ . Assuming this to be the uncertainty in the position of a proton in the nucleus, estimate the uncertainty in the proton's energy, in MeV. $\left( m _ { \text {proton } } = 1.67 \times 10 ^ { - 27 } \mathrm {~kg} , h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } , 1 \mathrm { eV } = 1.6 \times 10 ^ { - 19 } \mathrm {~J} \right.$ )

A) $0.6 \mathrm { MeV }$
B) $1.0 \mathrm { MeV }$
C) $0.4 \mathrm { MeV }$
D) $0.8 \mathrm { MeV }$