PreLab - Half-Life of Barium Name

A	N		No	t	l
Activity	Number of atoms		Original # of atoms	time	decay constant
A = ΔN / Δt		Define new term: Half-Life Time for the Activity to decay to ½ the original value
ΔN/Δt = -lN
ΔN/N = -l Δt		½Ao = Ao e^-^l^t1/2
**Integrate**		ln (½) = -l t1/2 (ln ½ = - ln 2)
N = No e^-^l^t		t1/2 = ln 2 / l
A = Ao e^-^l^t		t1/2 = 0.693 / l

Part A: Calibration (4 minute)		Please convert 88 count / 4 minutes to ??? counts / 30 sec to obtain background. Remember; if per unit time is 30 seconds for # of counts, then background per unit time must also be 30 seconds.
#Background Counts	Radiation LevelBackground
88

Part B: Unknown Material
Elapsed time	# of Counts	Activity (Count –Background)	ln (count-background) --optional--	Elapsed time	# of Counts	Activity (Count –Background)	ln (count-background) --optional--
1^st (0 to):30	567			6^th :330	159
2^nd(60 to):90	461			7^th :390	128
3^rd :150	333			8^th :450	105
4^th :210	281			9^th :510	79
5^th :270	202			10^th:570	61

In calculation section of procedures, it states to plot Activity vs time on semi-log paper.

An alternate method is to plot (natural log) of Activity vs time on linear (regular) graph paper and then use linefit.

What is l of the unknown material? Hints below: · Take the natural log of the equation, A = Ao e^-^l^t; finish displaying in slope-intercept form, (Given in lab manual: -l à slope ) y = m x + b ln(A) = + ln (A0)

What is the half life of the above unknown material?

3. (½) What is meant by metastable? a. stable, except when electrons are in contact with similar isotope b. stable, except in its half pure form c. stable portion between two radioactive forms d. unstable, but with a half life less than 10^-9 seconds e. none of the above

4. (½) In the above graph, the x-axis represents the time following each count interval. What would be different if the x-axis represents the time preceding each count intervals as in your lab? (similar to Question #8 in lab manual) a. The slope would be slightly higher b. The slope would be slightly lower c. The y-int would represent the Activity at the beginning of the 1^st time interval (Larger Activity) d. The y-int would represent the Activity at the ending of the 1^st time interval (Smaller Activity)