Define activation energy. What role does activation energy play in chemical kinetics?

A dealer’s profit, in units of $5000, on a new automobile is given by$Y = X^2$, where X is a random variable having the density function$f(x) = 2(1 − x), 0 \lt x \lt 1$,$f(x)=0$, elsewhere.

(a) Find the probability density function of the random variable Y.

(b) Using the density function of Y, find the probability that the profit on the next new automobile sold by this dealership will be less than$500.

$(a)$ Show that, as $n$ gets very large, the energy levels of the hydrogen atom get closer and closer together in energy. $(b)$ Do the radii of these energy levels also get closer together?

Find the momentum, kinetic energy, and total energy of a proton with speed (d) $0.99 c$.

The burning of methane in oxygen is a highly exothermic reaction. Yet a mixture of methane and oxygen gas can be kept indefinitely without any apparent change. Explain.

A proton's total energy is ten times its rest energy. How fast is it moving?

Suppose a hydrogen atom absorbs a photon of energy E, resulting in the transfer of the electron to a higher-energy level. Express the resulting change in the potential energy of the system in terms of E.

The sum of kinetic energy and potential energy of the particles in a material is $\underline{\phantom{\text{The horse .}}}$ .

If you try to increase the energy of a quantum harmonic oscillator by adding an amount of energy $\frac{1}{2} \hbar \sqrt{k_{s} / m},$ the energy doesn't increase. Why not?

How does energy become stored in a fossil fuel? What kind of energy is stored?

If energy cannot be destroyed, why do some people worry about the energy supply?

Distinguish What characteristics of water allow it to be used to produce energy as well as store energy?

By what factor is the Fermi energy higher than the $k T$ energy at room temperature?

Determine the wavelength and momentum of a photon whose energy equals the rest-mass energy of an electron.