H: Half Life W Bookmark this page In general a half-life is the time for a large number of particles of a single type to decrease by a factor of two as the particles decay into different particles. Here we use the symbol 7 for the half-life of the particles. Starting with NV particles of the same type, each having a half-life of 7, the number of particles decreases by a factor of two every passing of a half-life. t The goal is to calculate several quantities based on half-life. Number of Half Lives 10.0/10.0 points (graded) Calculate the number of half-lives n during a time interval of length t. Enter responses in terms of some or all of t fort, and tau for T. not t/tauNumber Remaining After Time 10.0/10.0 points (graded) Calculate the number of particles NV(t) remaining after the time t has passed. Enter responses in terms of some or all of n_t for nt, No for NV(0), t fort, and tau for T. N(t) N_0*e^(-In(2)*t/tau) No . e-In(2). SUBMIT You have used 9 of 10 attempts Distance in a Half-Life 10.0/10.0 points (graded) Now, let the particles all move with the same velocity v. Calculate the distance d, the particles move in one half-life. Enter responses in terms of some or all of v for v, d ford, t fort, and tau for T. dy = v*tauHalf Lives in Distance 10.0/10.0 points (graded) Now, let the particles all move with the same velocity v. Calculate the number of half-lives na that pass as the particles move a distance d. Enter responses in terms of some or all of v for v, d ford, d_(tau} ford,. nd d/d_{tau} SUBMIT You have used 1 of 10 attempts Number Remaining After Distance 0.0/10.0 points (graded) Calculate the number of particles NV(d) remaining after the the particles have moved the distance d. Enter responses in terms of some or all of v for v, d ford, d_{tau} ford,, n_d for nd, N_0 for N(0) N(d) N_0*(1- e^(-In(2)*d/d_{tau})) X No . ( 1 - e- In(2). 2