If there are 50 grams of u-238 on day zero of radioactive decay, how much will there be after 4.5 billion years

Aparticle of mass m is projected with an initial velocity v0 in a direction making an angle α with the horizontal level ground as shown in the figure. the motion of the particle occurs under a uniform gravitational field g pointing downward. (a) write down the lagrangian of the system by using the cartesian coordinates (x, y). (b) is there any cyclic coordinate(s). if so, interpret it (them) physically. (c) find the euler-lagrange equations. find at least one constant of motion. (d) solve the differential equation in part (c) and obtain x and y coordinates of the projectile as a function of time. (e) construct the hamiltonian of the system, h, and write down the hamilton’s equations (canonical equations) of motion.

If a substance is in the gas phase, which of qualities of the gas will stay constant? a: volume b: mass c: shape d: position of particles

The amount of heat required to change liquid water to vapor at its boiling temperature is 2256 kj/kg. the amount of heat required to change liquid mercury to its vapor state at its boiling temperature is 295 kj/kg. one kg of each substance is currently at its boiling point. how will the amount of thermal energy required to change each substance from a liquid to a gas differ?