Exam 28: Quantum Mechanics of Atoms

If the uncertainty in the position of a proton is $0.053 \mathrm {~nm}$ , what is the uncertainty in its speed? ( $h =$ $6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } , m _ { \text {proton } } = 1.67 \times 10 ^ { - 27 } \mathrm {~kg}$ )

An atom has completely filled inner shells and a single valence electron in an excited p state. The filled inner shells have an orbital momentum equal to zero. What is the magnitude of the orbital angular momentum of the atom?

The excited state of a certain atom is $3.2 \mathrm { eV } \pm 0.21 \mathrm { eV } . \left( h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } , 1 \mathrm { eV } = 1.60 \times \right.$ $10 ^ { - 19 } \mathrm {~J}$ ) (a) What is the average lifetime of this state, in femtoseconds? (b) If the excited energy were doubled (to $6.4 \mathrm { eV } \pm 0.21 \mathrm { eV }$ ), how would the lifetime be affected?

The orbital angular momentum quantum number ʆ can have any integer value ranging from

If $n = 5$ , which one of the following is not an allowed magnetic quantum number m₁?

Consider the $n = 10$ shell. (a) What is the largest value of the angular momentum quantum number, $l$ , in this shell? (b) How many electrons can be placed in this shell?

In its ground state, the quantum numbers $\left( n , l , m _ { 1 } , m _ { S } \right)$ for hydrogen are, respectively,

An atom has completely filled inner shells and a single valence electron in an excited $p$ state. The filled inner shells have an orbital momentum equal to zero. When a magnetic field is applied, what are the possible angles between the magnetic field and the orbital angular momentum?

If the maximum possible accuracy in measuring the velocity of a particle increases, the maximum possible accuracy in measuring its position will

The elements in the periodic table that have completely filled shells or subshells are referred to as

Consider ground-state helium having two electrons in orbit. If one of the electrons has quantum numbers $\left( n , \ell l , m _ { 1 } , m _ { s } \right)$ of $1,0,0 , - 1 / 2$ respectively, the quantum numbers for the other electron will be

How many 2d electron states can an atom have?

A laser produces a beam of $4000 - \mathrm { nm }$ light. A shutter allows a pulse of light, $30 \mathrm { ps }$ in duration, to pass through. What is the uncertainty in the energy of a photon in the pulse? $\left( 1 \mathrm { eV } = 1.60 \times 10 ^ { - 19 } \mathrm {~J} \right.$ , $h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s }$ )

If the maximum possible accuracy in measuring the lifetime of a particle increases, the maximum possible accuracy in measuring its energy will

How many unique quantum states correspond to the lowest possible energy level of an electron in the hydrogen atom?

In an excited hydrogen atom, the electron is in the $4 d$ state. If this atom is in an external magnetic field, what are the smallest and largest possible angles between the orbital angular momentum and the direction of the magnetic field (or any other direction, for that matter)?

If the maximum possible accuracy in measuring the position of a particle increases, the maximum possible accuracy in measuring its velocity will

An unstable particle produced in a high-energy collision is measured to have an energy of $483 \mathrm { MeV }$ and an uncertainty in energy of $29 \mathrm { keV }$ . Use the Heisenberg uncertainty principle to estimate the lifetime of this particle. $\left( h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } , 1 \mathrm { eV } = 1.60 \times 10 ^ { - 19 } \right)$

How many electrons will fit into a 4f subshell?

If the maximum possible accuracy in measuring the energy of a particle increases, the maximum possible accuracy in measuring its lifetime will