An energy of about 21 eV is required to excite an electron in a helium atom from the 1s state to the 2s state. The same transition for the $\mathrm{He}^{+}$ ion requires about twice as much energy. Explain why this is so.

Find the equilibrium vector for each transition matrix.

$$\left[\begin{array}{ccc} 0.5 & 0.2 & 0.3 \\ 0.1 & 0.4 & 0.5 \\ 0.3 & 0.1 & 0.6 \end{array}\right]$$

Provide a detailed arrow-pushing mechanism for the following transformation:

Draw a transition state that explains the stereochemical outcome.

Find the transition matrix from B to B$^\prime$

$$B=\{(2,-2),(6,3)\}, B^{\prime}=\{(1,1),(32,31)\}, \mathbf[{x}]_{B^{\prime}}=\left[\begin{array}{r} {2} \\ {-1} \end{array}\right]$$

Find the transition matrix from $B$ to $B^\prime$.

$$B=\{(-2,1),(1,-1)\},\quad B^\prime=\{(0,2),(1,1)\},\left[\bf{x}\right]_B=\left[6,-6\right]^r$$

Identify the function of the following in the body and classify each as an alkali metal, an alkaline earth metal, a transition element, or a halogen: I

Assume that f$^{\prime}$ and f$^{\prime \prime}$ exist for all x and let c be a critical point of function f. Show that f(x) cannot make a transition from $++$ to $-+$ at x=c. Hint: Apply the MVT to f$^{\prime}(x)$.

In the Bohr model for hydrogen, the radius of the $n$th orbit can be shown to be $n^2$ times the radius of the first Bohr orbit $r_1=0.05 \mathrm{~nm}$ (see Example 10.8). Similarly, the energy of an electron in the $n$th orbit is $\frac{1}{n^2}$ times its energy when in the $n=1$ orbit. What is the circunference of the $n=100$ orbit? (This is the distance the electron has traveled after having revolved around the proton once.) For such large- $n$ states, the orbital frequency is about equal to the frequency of the photon emitted in a transition from the $n$th level to an adjacent level with $n+1$ or $n-1$. Given this, find the frequency and corresponding period of the electron's orbit by computing the frequency associated with the transition from $n=100$ to $n=101$. Using your values for the electron's orbital size (distance) and travel time (period), calculate the approximate speed of the electron in the 100 th orbit. How does this speed compare to the speed of light?

In the following exercise, find the steady-state matrix for the transition matrix.

$$\left[\begin{array}{rr}.6 & .3 \\ .4 & .7\end{array}\right]$$

In the following exercise, find the steady-state matrix for the transition matrix.

$$\left[\begin{array}{rr}.5 & .4 \\ .5 & .6\end{array}\right]$$

Distinguish between an excellent metallic conductor of electricity (such as silver) and a superconducting substance (such as $\mathrm{Nb}_3 \mathrm{Sn}$ ) below its superconducting transition temperature.

Which of the following is not one of the four gates in the RUP methodology?

a. Elaboration

b. Collaboration

c. Construction

d. Transition

Draw a plausible transition state for the bimolecular reaction of nitric oxide with ozone. Use dashed lines to indicate the atoms that are weakly linked together in the transition state.

$$\mathrm{NO}(g)+\mathrm{O}_3(g) \longrightarrow \mathrm{NO}_2(g)+\mathrm{O}_2(g)$$

Suppose $V$ is the space spanned by $\mathbf{f}_1=\sin x$ and $\mathbf{f}_2=\cos x$. Determine the transition matrix from $B$ to $B^{\prime}$.