**Core Concept**
The diagnosis of ectopic pregnancy often relies on the measurement of beta-human chorionic gonadotropin (β-hCG) levels in the blood. A key principle in diagnosing ectopic pregnancy is identifying when β-hCG levels are insufficient to sustain an intrauterine pregnancy, often due to the abnormal implantation of the fertilized ovum outside the uterus.

**Why the Correct Answer is Right**
In cases of ectopic pregnancy, the β-hCG levels may not reach the threshold necessary to sustain an intrauterine pregnancy. A β-hCG level of more than 6500 mIU/mL on a transvaginal ultrasound examination is generally considered sufficient to rule out an ectopic pregnancy. This is because β-hCG levels below this threshold may indicate an abnormal implantation of the fertilized ovum outside the uterus. The production of β-hCG is crucial for maintaining the corpus luteum, which in turn supports the early development of the embryo.

**Why Each Wrong Option is Incorrect**
**Option A:** A β-hCG level of 5000 mIU/mL may be insufficient for diagnosing ectopic pregnancy, as it is still within the range that can be associated with a normal intrauterine pregnancy.
**Option B:** A β-hCG level of 3000 mIU/mL is too low to rule out ectopic pregnancy, as it is within the range that can be associated with an abnormal implantation of the fertilized ovum outside the uterus.
**Option C:** A β-hCG level of 9000 mIU/mL is higher than the threshold for ruling out ectopic pregnancy, but it is not the correct answer as it is still within the range that can be associated with an intrauterine pregnancy.

**Clinical Pearl / High-Yield Fact**
A β-hCG level of more than 6500 mIU/mL on a transvaginal ultrasound examination is generally considered sufficient to rule out ectopic pregnancy, but it is essential to consider other clinical factors, such as a history of pelvic surgery, previous ectopic pregnancy, or a history of infertility.

**Correct Answer: C. 6500 mIU/mL**