In 1999, quantum interference was observed in a beam of so-called buckyballs: carbon molecules with the formula c60 and the shape of a soccer ball.
a) the wavelength observed was about 3 pm. how fast were the molecules moving?
b) what would be the wavelength of an electron moving at the same speed?
c) numerically justify the neglect of relativistic effects in this problem.

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

This punnett square shows the cross between two pants. one parent has round seeds (rr). and the other parent has wrinkled seeds (rr) which best describes their offspring as shown in this cross?

The second largest public utility in the nation is the sole provider of electricity in 32 counties of southern florida. to meet the monthly demand for electricity in these counties, which is given by the inverse demand function p = 1,200 – 4q, the utility company has set up two electric generating facilities: q1 kilowatts are produced at facility 1, and q2 kilowatts are produced at facility 2 (so q = q1 + q2). the costs of producing electricity at each facility are given by c1(q1) = 8,000 + 6q12 and c2(q2) = 6,000 + 3q22, respectively. determine the profit-maximizing amounts of electricity to produce at the two facilities, the optimal price, and the utility company’s profit