In a clinical trial, the treatment effect $\Delta = \mu_1 - \mu_2$ is estimated using a sample size $n=100$. If the observed standard error is $SE = 0.5$, and we perform a two-sided test $H_0: \Delta = 0$ against $H_a: \Delta \neq 0$, at what specific value of $\Delta$ would the power of the test be exactly $0.5$ at a significance level of $\alpha = 0.05$?