Solving Young Sheldon's 100th episode vanity card Please define the terms. Below is Chuck Lorre's 700th vanity card which congratulates Young Sheldon on reaching 100 episodes.

Part 1. Find $x$ in $J_0(x)=0$. --> I guess this refers to Bessel of the 1st kind, but wolfram alpha doesn't give me a unique answer. What's going on? I forgot this already. I just remember in calculus class that Bessel is like a series solution to some ordinary differential equation.

I somehow think we're supposed to have $x=2.4041$ and so $yz^2 = 10$ or something.
Part 2. $y=R_y$ --> I guess this refers to Rydberg constant (Rydberg unit of energy). Soooo $y = 2.1798723611035 \times 10^{-18}$ ?
Part 3. $z = \frac{\mu_D}{\mu_N}$.

*

*2.1. $\mu_N$ I guess is nuclear magneton?


*3.2. As for $\mu_D$, no idea. Wasn't able to find in the list of physical constants except possibly...Bohr magneton ($\mu_B$) ? Or maybe $z$ is the W-to-Z mass ratio?
 A: So let us assume, following the OP, that $x$ is the root of the Bessel function $J_0(x)$. This function has a lot of roots, but we choose the minimum positive one $x\approx 2.40483$. Let us follow the OP further and assume that $y$ is indeed the Rydberg constant, but in electronvolts, so $y\approx 13.6056980659$. Let us also assume that $z$ is the ratio of the magnetic moments of the deuteron and the neutron, so $z\approx 0.8574382338$. Then $$(y\cdot z^2)^{x-0.4041}\approx 100.226.$$ Not quite 100, but close. One gets approximately 100.0 with the following values:

*

*$x=2.4041$ (not quite correct, but the card implies this is what its creator used)


*$y=13.605$


*$z=0.8574$.
EDIT (April 9, 2022): @BCLC has pointed to my mistake: 0.8574382338 is not "the ratio of the magnetic moments of the deuteron and the neutron", but "deuteron magnetic moment to nuclear magneton ratio". However, the notation is still $\mu_d/\mu_N$.
A: This is how I solved it on 1 April.
Here are the essential details: x = 2.4048 (the first zero crossing of an order zero Bessel function), y = 13.606 (the Rydberg unit of energy in eV) and z = 0.857 (the ratio of deuterium’s magnetic dipole moment to the nuclear magneton value). The answer is 100.0 to four significant digits. Further details, as well as notes on the nonsensical units can be found in the linked PDF (which will not change, and should be read with an awareness of Young Sheldon’s subject matter and the document's publication date).
Note that the number 1648777428 is a Unix timestamp.  The Young Sheldon Episode Count equation only works for that one episode, so I specify the date of the episode's first airing to distinguish it from any future YSEC equation.
