Exam 28: Quantum Mechanics of Atoms

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. $\left( m _ { \text {proton } } = 1.67 \times 10 ^ { - 27 } \mathrm {~kg} , h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } , 1 \mathrm { eV } = 1.6 \times 10 ^ { - 19 } \mathrm {~J} \right.$ )

If an electron is determined to be at $x = 2.000 \mathrm {~cm} \pm 0.0010 \mathrm {~cm}$ , what is the minimum uncertainty in the $x$ component of its velocity? (melectron $= 9.11 \times 10 ^ { - 31 } \mathrm {~kg} , h = 6.626 \times$ $10 - 34 \mathrm {~J} \cdot \mathrm { s }$ )

What is the atomic number of a neutral atom that has an electron configuration of $1 s ^ { 2 } 2 s ^ { 2 } 2 p ^ { 6 } 3 s ^ { 2 }$ $3 p ^ { 2 }$ ?

You measure the velocity of an electron to an accuracy of $\pm 22.6 \mathrm {~m} / \mathrm { s }$ . What is the minimum uncertainty in its position? $\left( h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } , m _ { \text {electron } } = 9.11 \times 10 ^ { - 31 } \mathrm {~kg} \right)$

An electron is known to be confined to a region of width $0.10 \mathrm {~nm}$ . What is an approximate value for the least kinetic energy it could have, in electron-volts? $\left( h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } , 1 \mathrm { eV } = 1.60 \times \right.$ $10 ^ { - 19 } \mathrm {~J} , \left( m _ { \text {electron } } = 9.11 \times 10 ^ { - 31 } \mathrm {~kg} \right.$ )

Which one of the following is the correct electronic configuration for the sodium atom, which has 11 electrons?

A molecule of roughly spherical shape has a mass of $1.80 \times 10 ^ { - 25 } \mathrm {~kg}$ and a diameter of $0.6 \mathrm {~nm}$ . If the uncertainty in the measured position of the molecule is equal to the molecular diameter, what is the minimum uncertainty in the speed of the molecule? ( $h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s }$ )

In a hydrogen atom, a given electron has $\ell = 7$ . How many possible values can $m _ { 1 }$ have?

A measurement of an electron's speed is $2.0 \times 10 ^ { 6 } \mathrm {~m} / \mathrm { s }$ and has an uncertainty of $10 \%$ . What is the minimum uncertainty in the position of the electron? $\left( m _ { \text {electron } } = 9.11 \times 10 ^ { - 31 } \mathrm {~kg} , h = 6.626 \times \right.$ $\left. 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } \right)$

An electron is trapped in a quantum well that is $48.6 \mathrm {~nm}$ wide. Calculate the minimum uncertainty in its velocity. $\left( h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } , m _ { \text {electron } } = 9.11 \times 10 ^ { - 31 } \mathrm {~kg} \right)$

For the ground state of the hydrogen atom, which of the following numbers represents the correct value of the magnetic quantum number?

Suppose that the speed of an electron traveling $1.0 \mathrm {~km} / \mathrm { s }$ is known to an accuracy of 1 part in 10,000 (that is, within $0.01 \%$ ). What is the minimum uncertainty in the position of this electron? $\left( m _ { \mathrm { e } } \right.$ ectron $\left. = 9.11 \times 10 ^ { - 31 } \mathrm {~kg} , h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } \right)$

Which one of the following is the correct electronic configuration for carbon, which has 6 electrons?

How many values of the magnetic quantum number, $m \ell$ , are possible if the orbital angular momentum quantum number is $\ell = 2$ ?