Which action MOST LIKELY occurred in order for the sugar to dissolve?

The de broglie relation λ=h/p can be rewritten in terms of the wave number k as p=kℏ. recall that wave number is defined by k=2π/λ. using the fact that λ=v/f, find the wave numbers k1 and k2 corresponding to frequencies f1 and f2. express your answer as two expressions

Two identical small charged spheres are a certain distance apart, and each one initially experiences an electrostatic force of magnitude f due to the other. with time, charge gradually leaks off of both spheres. when each of the spheres has lost half its initial charge, the magnitude of the electrostatic force will be

Which of the following are not typically included in the periodic table? a. atomic mass b. element symbol c. isotopes d. number of electrons