Why does a heavier element have a low specific heat capacity? Lead has 207 amu and 125j/kg/c while copper has 63 amu and 376 j/kg/c, why is that? So if energy is stored in the motion of the particles, heavier particles should move slower and therefore wouldn't this means that it require more energy to increase the temperature by 1-degree Celcius? I looked up on google and the main reason it said is that there are more particles, but how? I am taking 1 kg of lead and 1 kg of copper, and from my understanding, their masses are different because the lead particles are heavier instead of more of particles in lead than copper. So please explain why does a heavier element tend to have a low specific heat capacity?
 A: I think you mean to say that they have a different number of particles- 1kg of lead and 1kg of copper surely have the same mass. 
There are $~2.91\times10^{24}$ atoms in a kg of lead, and $~9.45\times10^{24}$ atoms in a kg of copper. Heat (more accurately, thermal energy) is "stored" in the particular degrees of freedom for the motion of the atomic "particles"- and since there are more atoms in a kilogram of copper, it's gonna have more atoms with more degrees of freedom. Thus, more capacity for storage.  
A: 
Lead has 207 amu and 125j/kg/c while copper has 63 amu and 376 j/kg/c, why is that?

Because lead has a higher atomic mass, but that isn't a very complete answer.

So if energy is stored in the motion of the particles, heavier particles should move slower and therefore wouldn't this means that it require more energy to increase the temperature by 1-degree Celcius?

No. Temperature is a measure of the average kinetic energy, not the average velocity.
Okay but still why a difference? You have to consider that copper has a lower standard atomic weight thus for 1kg of copper the amount of substance is more than the for 1kg of lead (i.e. 3 times more atoms in 1kg of copper than 1kg of lead). Think: a pound of bricks and a pound of feathers have the same mass, but it takes many more feather feathers than bricks to make that one pound.
Temperature is the average kinetic energy on a per atom/particle basis. For any given atom/particle with a given energy the temperature can be calculated. If a particle has more energy, it has a higher temperature, if you have two particles that weight half as much and have half as much energy as the initial particle then even though in aggregate they have the same mass and energy, the total energy is the same, but the average energy is half thus the temperature is lower. 
If you look at metals on a atomic basis you will find that the molar specific heat of metals can be approximated by the Dulong-Petit Law to be: $C_v \approx 3R$ where $R$ is the ideal gas constant and $C_v$ is a molar heat capacity. Again this is an approximation, but the values are much close as copper has a $C_v$ of $24.6~\mathrm{J~mol^{-1}~K^{-1}}$ and lead has a $C_v$ of $26.5~\mathrm{J~mol^{-1}~K^{-1}}$.
If you want to approximate a specific heat capacity based on weight just divide $3R$ by the standard atomic weight ($A_r$):
$$C_v(\text{mass}) = \frac{3R}{A_r}$$
