Final answer:
The nurse should continue to administer lithium carbonate as prescribed, as a serum lithium level of 1 mEq/L is within the therapeutic range for treating bipolar disorder.
Step-by-step explanation:
If the client's serum lithium level is 1 mEq/L one week after starting lithium carbonate therapy for bipolar disorder, the nurse should continue to administer the medication as ordered. Therapeutic levels of lithium for the management of bipolar disorder typically range from 0.6 to 1.2 mEq/L. Therefore, a level of 1 mEq/L is within the therapeutic range and does not indicate toxicity. However, it is essential for the nurse to observe the client closely for signs and symptoms of lithium toxicity as part of ongoing monitoring.