Variance scaling for a difference of two sample means

Let $X_1,…,X_{10}$ be a random sample from a $N(3,12)$ population. Suppose $Y_1=\frac16\sum_{i=1}^6X_i$ and $Y_2=\frac14\sum_{i=7}^{10}X_i$. If $\frac{(Y_1-Y_2)^2}\alpha$ has a $\chi^2_1$ distribution, then the value of $\alpha$ is _______________